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Geometric configurations of singularities of planar polynomial differential systems : a global classification in the quadratic case / / Joan C. Artés [et al.]
| Geometric configurations of singularities of planar polynomial differential systems : a global classification in the quadratic case / / Joan C. Artés [et al.] |
| Autore | Artés Joan C. <1961-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (xii, 699 pages) |
| Disciplina | 514.746 |
| Soggetto topico |
Singularities (Mathematics)
Polynomials Differential equations Singularitats (Matemàtica) Polinomis Equacions diferencials |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-50570-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I Polynomial differential systems with emphasis on the quadratic ones 1 Introduction 2 Survey of results on quadratic differential systems 3 Singularities of polynomial differential systems 4 Invariants in mathematical classification problems 5 Invariant theory of planar polynomial vector fields 6 Main results on classifications of singularities in QS 7 Classifications of quadratic systems with special singularities Part II 8 QS with finite singularities of total multiplicity at most one 9 QS with finite singularities of total multiplicity two 10 QS with finite singularities of total multiplicity three 11 QS with finite singularities of total multiplicity four 12 Degenerate quadratic systems 13 Conclusions |
| Record Nr. | UNINA-9910485593103321 |
Artés Joan C. <1961->
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric configurations of singularities of planar polynomial differential systems : a global classification in the quadratic case / / Joan C. Artés [et al.]
| Geometric configurations of singularities of planar polynomial differential systems : a global classification in the quadratic case / / Joan C. Artés [et al.] |
| Autore | Artés Joan C. <1961-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (xii, 699 pages) |
| Disciplina | 514.746 |
| Soggetto topico |
Singularities (Mathematics)
Polynomials Differential equations Singularitats (Matemàtica) Polinomis Equacions diferencials |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-50570-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I Polynomial differential systems with emphasis on the quadratic ones 1 Introduction 2 Survey of results on quadratic differential systems 3 Singularities of polynomial differential systems 4 Invariants in mathematical classification problems 5 Invariant theory of planar polynomial vector fields 6 Main results on classifications of singularities in QS 7 Classifications of quadratic systems with special singularities Part II 8 QS with finite singularities of total multiplicity at most one 9 QS with finite singularities of total multiplicity two 10 QS with finite singularities of total multiplicity three 11 QS with finite singularities of total multiplicity four 12 Degenerate quadratic systems 13 Conclusions |
| Record Nr. | UNISA-996466413203316 |
|
Artés Joan C. <1961->
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Handbook of geometry and topology of singularities II / / José Luis Cisneros-Molina, Dũng Tráng Lê, José Seado, editors
| Handbook of geometry and topology of singularities II / / José Luis Cisneros-Molina, Dũng Tráng Lê, José Seado, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (581 pages) |
| Disciplina | 516.35 |
| Soggetto topico |
Singularities (Mathematics)
Geometry, Algebraic Topological groups Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-78024-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Contributors -- 1 The Analytic Classification of Irreducible Plane Curve Singularities -- 1.1 Background -- 1.1.1 Plane Curve Singularities -- 1.1.2 Irreducible Plane Curve Singularities -- 1.1.3 Equisingularity of Branches -- 1.1.4 Semiroots of a Branch -- 1.2 Zariski's Approach -- 1.2.1 A Parameter Space -- 1.2.2 Kähler Differentials -- 1.2.3 The Zariski Invariant -- 1.3 Singularity Theory Approach -- 1.3.1 The Complete Transversal Theorem -- 1.3.2 Tangent Spaces to Orbits -- 1.3.3 The Analytic Classification -- 1.4 Final Remarks -- 1.4.1 Comparison with Other Works -- 1.4.2 Computability -- 1.4.3 A Solution for the Moduli Problem -- 1.4.4 Dimensions of Components of the Moduli Space -- 1.4.5 An Example -- 1.4.6 Analytic Versus Formal -- References -- 2 Plane Algebraic Curves with Prescribed Singularities -- 2.1 Introduction -- 2.1.1 Preliminaries: Isolated Singularities -- 2.2 Singular Plane Curves: Restrictions -- 2.2.1 Genus Formula and Bézout's Theorem -- 2.2.2 Plücker Formulae -- 2.2.3 Log-Miyaoka-Yau Inequality -- 2.2.4 Spectral Bound -- 2.3 Plane Curves with Nodes and Cusps -- 2.3.1 Plane Curves with Nodes -- 2.3.2 Plane Curves with Nodes and Cusps -- 2.4 Plane Curves with Arbitrary Singularities -- 2.4.1 Curves of Small Degrees -- 2.4.2 Curves with Simple, Ordinary, and Semi-quasihomogeneous Singularities -- 2.4.3 Curves with Arbitrary Singularities -- 2.5 Related and Open Problems -- 2.5.1 Existence Versus T-Smoothness and Irreducibility -- 2.5.2 Curves on Other Algebraic Surfaces -- 2.5.3 Other Related Problems -- 2.5.4 Some Questions and Conjectures -- References -- 3 Limit of Tangents on Complex Surfaces -- 3.1 Introduction -- 3.2 An Application of a Theorem of Hironaka -- 3.2.1 The Thom Stratification -- 3.2.2 Deformation on the Tangent Cone -- 3.2.3 Proof of Corollary 3.2.3.
3.3 The Theorem of Teissier -- 3.3.1 Statement -- 3.4 Hypersurfaces of Dimension 2 -- 3.4.1 Consequences of Teissier's Theorem -- 3.4.2 Limit of Tangents of Surfaces of mathbbC3 with Isolated Singularity -- 3.5 Polar Varieties of a Hypersurface of Dimension 2 -- 3.5.1 Polar Varieties -- 3.5.2 Exceptional Tangents of a Hypersurface of Dimension 2 -- 3.6 Surfaces in CN -- 3.6.1 Description of the Limits -- 3.6.2 Polar Curves -- 3.6.3 Relation with Discriminants of Projections to mathbbC2 -- 3.6.4 Exceptional Tangents and Equisingularity -- 3.6.5 Surfaces Without Exceptional Tangents -- 3.7 Appendix: Intersections in Grassmannians -- References -- 4 Algebro-Geometric Equisingularity of Zariski -- 4.1 Introduction -- 4.2 Equisingular Families of Plane Curve Singularities -- 4.2.1 Equisingular Families of Plane Curve Singularities. Definition -- 4.2.2 Equisingular Families of Plane Curve Singularities and Puiseux with Parameter -- 4.3 Zariski Equisingularity in Families -- 4.3.1 Topological Equisingularity and Topological Triviality -- 4.3.2 Arc-Wise Analytic Triviality -- 4.3.3 Whitney Fibering Conjecture -- 4.3.4 Algebraic Case -- 4.3.5 Principle of Generic Topological Equisingularity -- 4.3.6 Zariski's Theorem on the Fundamental Group -- 4.3.7 General Position Theorem -- 4.4 Construction of Equisingular Deformations -- 4.4.1 Global Polynomial Case -- 4.4.2 Application: Algebraic Sets are Homeomorphic to Algebraic Sets Defined Over Algebraic Number Fields -- 4.4.3 Analytic Case -- 4.4.4 Application: Analytic Set Germs are Homeomorphic to Algebraic Ones -- 4.4.5 Equisingularity of Function Germs -- 4.4.6 Local Topological Classification of Smooth Mappings -- 4.5 Equisingularity Along a Nonsingular Subspace. Zariski's Dimensionality Type -- 4.5.1 Equimultiplicity. Transversality of Projection. 4.5.2 Relation to Other Equisingularity Conditions. Examples -- 4.5.3 Lipschitz Equisingularity -- 4.5.4 Zariski Dimensionality Type. Motivation -- 4.5.5 Zariski Dimensionality Type -- 4.5.6 Almost all Projections -- 4.5.7 Canonical Stratification of Hypersurfaces -- 4.5.8 Zariski Equisingularity and Equiresolution of Singularities -- 4.6 Appendix. Generalized Discriminants -- References -- 5 Intersection Homology -- 5.1 Introduction -- 5.2 Classical Results-Poincaré and Poincaré-Lefchetz -- 5.2.1 PL-Structures -- 5.2.2 Pseudomanifolds -- 5.2.3 Stratifications -- 5.2.4 Borel-Moore Homology -- 5.2.5 Poincaré Duality Homomorphism -- 5.2.6 Poincaré-Lefschetz Homomorphism -- 5.3 The Useful Tools: Sheaves-Derived Category -- 5.3.1 Sheaves -- 5.3.2 System of Local Coefficients -- 5.3.3 Complexes of Sheaves -- 5.3.4 Injective Resolutions -- 5.3.5 Hypercohomology -- 5.3.6 The (Constructible) Derived Category -- 5.3.7 Derived Functors -- 5.3.8 Dualizing Complex -- 5.4 Intersection Homology-Geometric and Sheaf Definitions -- 5.4.1 The Definition for PL-Stratified Pseudomanifolds -- 5.4.2 Definition with Local Systems -- 5.4.3 Witt Spaces -- 5.4.4 The Intersection Homology Sheaf Complex -- 5.4.5 The Deligne Construction -- 5.4.6 Local Calculus and Consequences -- 5.4.7 Characterizations of the Intersection Complex -- 5.5 Main Properties of Intersection Homology -- 5.5.1 First Properties -- 5.5.2 Functoriality -- 5.5.3 Lefschetz Fixed Points and Coincidence Theorems -- 5.5.4 Morse Theory -- 5.5.5 De Rham Theorems -- 5.5.6 Steenrod Squares, Cobordism and Wu Classes -- 5.6 Supplement: More Applications and Developments -- 5.6.1 Toric Varieties -- 5.6.2 The Asymptotic Set -- 5.6.3 Factorization of Poincaré Morphism for Toric Varieties -- 5.6.4 General Perversities -- 5.6.5 Equivariant Intersection Cohomology -- 5.6.6 Intersection Spaces. 5.6.7 Blown-Up Intersection Homology -- 5.6.8 Real Intersection Homology -- 5.6.9 Perverse Sheaves and Applications -- References -- 6 Milnor's Fibration Theorem for Real and Complex Singularities -- 6.1 Introduction -- 6.2 Exotic Spheres and the Birth of Milnor's Fibration -- 6.2.1 Singularities and Exotic Spheres -- 6.2.2 Open Questions -- 6.3 Model Example: the Brieskorn-Pham Singularities -- 6.3.1 Weighted Homogeneous Singularities -- 6.3.2 Real Analytic Singularities -- 6.4 Local Conical Structure of Analytic Sets -- 6.5 The Classical Fibration Theorems for Complex Singularities -- 6.6 Topology of the Link and the Fiber -- 6.6.1 The Link -- 6.6.2 The Fiber -- 6.6.3 Vanishing Cycles, Open-Books and the Monodromy -- 6.7 Extensions and Refinements of Milnor's Fibration Theorem -- 6.8 Milnor Fibration for Real Analytic Maps -- 6.8.1 Strong Milnor Condition -- 6.8.2 Model Singularities -- 6.9 On Functions with a Non-isolated Critical Point -- 6.9.1 Functions with an Isolated Critical Value -- 6.9.2 Polar Weighted Singularities -- 6.9.3 Functions with Arbitrary Discriminant -- 6.10 Milnor Fibrations and d-Regularity -- 6.10.1 The Case of an Isolated Critical Value -- 6.10.2 The General Case -- 6.11 Singularities of Mixed Functions -- References -- 7 Lê Cycles and Numbers of Hypersurface Singularities -- 7.1 Introduction and Earlier Results -- 7.2 Definitions and Basic Properties of Lê Cycles and Numbers -- 7.3 Lê Numbers and the Topology of the Milnor Fiber -- 7.4 Lê-Iomdine Formulas and Thom's Af Condition -- 7.5 Aligned Singularities and Hyperplane Arrangements -- 7.6 Other Characterizations of the Lê Cycles -- 7.7 Projective Lê Cycles -- References -- 8 Introduction to Mixed Hypersurface Singularity -- 8.1 A Quick Trip to the Complex Hypersurface Singularity Theory -- 8.1.1 Milnor Fibration -- 8.1.2 The Hamm-Lê lemma and a Tubular Milnor Fibration. 8.1.3 Weighted Homogeneous Polynomials -- 8.1.4 Newton Boundary and Non-degeneracy -- 8.2 Mixed Hypersurface Singularities -- 8.2.1 Mixed Analytic Functions -- 8.2.2 Mixed Singularities -- 8.2.3 A Tubular Milnor Fibration of a Real Analytic Mapping -- 8.2.4 Stratification and Thom's af-Regularity -- 8.3 Milnor Fibrations for Mixed Functions -- 8.3.1 Mixed Functions and Newton Boundary -- 8.3.2 Non-degeneracy of Mixed Functions -- 8.3.3 Mixed Functions of one Variable (n=1) -- 8.3.4 Mixed Weighted Homogeneous Polynomials -- 8.3.5 Milnor Fibrations for Strongly Non-degenerate Mixed Functions -- 8.3.6 The Milnor Fibration for Convenient Mixed Functions -- 8.3.7 The Spherical Milnor Fibration -- 8.3.8 Milnor Fibrations for Non-convenient Mixed Functions -- 8.3.9 Topological Stability -- 8.3.10 Equivalence of Tubular and Spherical Milnor Fibrations -- 8.3.11 Real Blowing Up and a Resolution of a Real Type -- 8.3.12 Simplicial Mixed Polynomials -- 8.3.13 The Join Theorem -- 8.3.14 Topology of the Milnor Fiber -- 8.3.15 The Milnor Fibration for fbarg -- 8.3.16 Mixed Projective Hypersurfaces -- 8.3.17 Remarks and Problems -- References -- 9 From Singularities to Polyhedral Products -- 9.1 Introduction -- 9.2 Singularity Theory -- 9.3 Dynamical Systems -- 9.3.1 Complex Differential Equations -- 9.3.2 Higher Dimensional Group Actions -- 9.3.3 Generalized Hopf Bifurcations -- 9.4 Geometry -- 9.4.1 Complex Geometry -- 9.4.2 Contact and Symplectic Geometry -- 9.5 To the Polyhedral Product Functor -- 9.5.1 Coxeter Groups, Small Covers and Toric Manifolds -- 9.5.2 The Polyhedral Product Functor -- 9.6 Back to Singularity Theory -- 9.6.1 Quadratic Cones -- 9.6.2 Singular Intersections and Smoothings -- References -- 10 Complements to Ample Divisors and Singularities -- 10.1 Introduction. 10.2 Braid Monodromy, Presentations of Fundamental Groups and Sufficient Conditions for Commutativity. |
| Record Nr. | UNISA-996466405403316 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Handbook of geometry and topology of singularities II / / José Luis Cisneros-Molina, Dũng Tráng Lê, José Seado, editors
| Handbook of geometry and topology of singularities II / / José Luis Cisneros-Molina, Dũng Tráng Lê, José Seado, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (581 pages) |
| Disciplina | 516.35 |
| Soggetto topico |
Singularities (Mathematics)
Geometry, Algebraic Topological groups Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-78024-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Contributors -- 1 The Analytic Classification of Irreducible Plane Curve Singularities -- 1.1 Background -- 1.1.1 Plane Curve Singularities -- 1.1.2 Irreducible Plane Curve Singularities -- 1.1.3 Equisingularity of Branches -- 1.1.4 Semiroots of a Branch -- 1.2 Zariski's Approach -- 1.2.1 A Parameter Space -- 1.2.2 Kähler Differentials -- 1.2.3 The Zariski Invariant -- 1.3 Singularity Theory Approach -- 1.3.1 The Complete Transversal Theorem -- 1.3.2 Tangent Spaces to Orbits -- 1.3.3 The Analytic Classification -- 1.4 Final Remarks -- 1.4.1 Comparison with Other Works -- 1.4.2 Computability -- 1.4.3 A Solution for the Moduli Problem -- 1.4.4 Dimensions of Components of the Moduli Space -- 1.4.5 An Example -- 1.4.6 Analytic Versus Formal -- References -- 2 Plane Algebraic Curves with Prescribed Singularities -- 2.1 Introduction -- 2.1.1 Preliminaries: Isolated Singularities -- 2.2 Singular Plane Curves: Restrictions -- 2.2.1 Genus Formula and Bézout's Theorem -- 2.2.2 Plücker Formulae -- 2.2.3 Log-Miyaoka-Yau Inequality -- 2.2.4 Spectral Bound -- 2.3 Plane Curves with Nodes and Cusps -- 2.3.1 Plane Curves with Nodes -- 2.3.2 Plane Curves with Nodes and Cusps -- 2.4 Plane Curves with Arbitrary Singularities -- 2.4.1 Curves of Small Degrees -- 2.4.2 Curves with Simple, Ordinary, and Semi-quasihomogeneous Singularities -- 2.4.3 Curves with Arbitrary Singularities -- 2.5 Related and Open Problems -- 2.5.1 Existence Versus T-Smoothness and Irreducibility -- 2.5.2 Curves on Other Algebraic Surfaces -- 2.5.3 Other Related Problems -- 2.5.4 Some Questions and Conjectures -- References -- 3 Limit of Tangents on Complex Surfaces -- 3.1 Introduction -- 3.2 An Application of a Theorem of Hironaka -- 3.2.1 The Thom Stratification -- 3.2.2 Deformation on the Tangent Cone -- 3.2.3 Proof of Corollary 3.2.3.
3.3 The Theorem of Teissier -- 3.3.1 Statement -- 3.4 Hypersurfaces of Dimension 2 -- 3.4.1 Consequences of Teissier's Theorem -- 3.4.2 Limit of Tangents of Surfaces of mathbbC3 with Isolated Singularity -- 3.5 Polar Varieties of a Hypersurface of Dimension 2 -- 3.5.1 Polar Varieties -- 3.5.2 Exceptional Tangents of a Hypersurface of Dimension 2 -- 3.6 Surfaces in CN -- 3.6.1 Description of the Limits -- 3.6.2 Polar Curves -- 3.6.3 Relation with Discriminants of Projections to mathbbC2 -- 3.6.4 Exceptional Tangents and Equisingularity -- 3.6.5 Surfaces Without Exceptional Tangents -- 3.7 Appendix: Intersections in Grassmannians -- References -- 4 Algebro-Geometric Equisingularity of Zariski -- 4.1 Introduction -- 4.2 Equisingular Families of Plane Curve Singularities -- 4.2.1 Equisingular Families of Plane Curve Singularities. Definition -- 4.2.2 Equisingular Families of Plane Curve Singularities and Puiseux with Parameter -- 4.3 Zariski Equisingularity in Families -- 4.3.1 Topological Equisingularity and Topological Triviality -- 4.3.2 Arc-Wise Analytic Triviality -- 4.3.3 Whitney Fibering Conjecture -- 4.3.4 Algebraic Case -- 4.3.5 Principle of Generic Topological Equisingularity -- 4.3.6 Zariski's Theorem on the Fundamental Group -- 4.3.7 General Position Theorem -- 4.4 Construction of Equisingular Deformations -- 4.4.1 Global Polynomial Case -- 4.4.2 Application: Algebraic Sets are Homeomorphic to Algebraic Sets Defined Over Algebraic Number Fields -- 4.4.3 Analytic Case -- 4.4.4 Application: Analytic Set Germs are Homeomorphic to Algebraic Ones -- 4.4.5 Equisingularity of Function Germs -- 4.4.6 Local Topological Classification of Smooth Mappings -- 4.5 Equisingularity Along a Nonsingular Subspace. Zariski's Dimensionality Type -- 4.5.1 Equimultiplicity. Transversality of Projection. 4.5.2 Relation to Other Equisingularity Conditions. Examples -- 4.5.3 Lipschitz Equisingularity -- 4.5.4 Zariski Dimensionality Type. Motivation -- 4.5.5 Zariski Dimensionality Type -- 4.5.6 Almost all Projections -- 4.5.7 Canonical Stratification of Hypersurfaces -- 4.5.8 Zariski Equisingularity and Equiresolution of Singularities -- 4.6 Appendix. Generalized Discriminants -- References -- 5 Intersection Homology -- 5.1 Introduction -- 5.2 Classical Results-Poincaré and Poincaré-Lefchetz -- 5.2.1 PL-Structures -- 5.2.2 Pseudomanifolds -- 5.2.3 Stratifications -- 5.2.4 Borel-Moore Homology -- 5.2.5 Poincaré Duality Homomorphism -- 5.2.6 Poincaré-Lefschetz Homomorphism -- 5.3 The Useful Tools: Sheaves-Derived Category -- 5.3.1 Sheaves -- 5.3.2 System of Local Coefficients -- 5.3.3 Complexes of Sheaves -- 5.3.4 Injective Resolutions -- 5.3.5 Hypercohomology -- 5.3.6 The (Constructible) Derived Category -- 5.3.7 Derived Functors -- 5.3.8 Dualizing Complex -- 5.4 Intersection Homology-Geometric and Sheaf Definitions -- 5.4.1 The Definition for PL-Stratified Pseudomanifolds -- 5.4.2 Definition with Local Systems -- 5.4.3 Witt Spaces -- 5.4.4 The Intersection Homology Sheaf Complex -- 5.4.5 The Deligne Construction -- 5.4.6 Local Calculus and Consequences -- 5.4.7 Characterizations of the Intersection Complex -- 5.5 Main Properties of Intersection Homology -- 5.5.1 First Properties -- 5.5.2 Functoriality -- 5.5.3 Lefschetz Fixed Points and Coincidence Theorems -- 5.5.4 Morse Theory -- 5.5.5 De Rham Theorems -- 5.5.6 Steenrod Squares, Cobordism and Wu Classes -- 5.6 Supplement: More Applications and Developments -- 5.6.1 Toric Varieties -- 5.6.2 The Asymptotic Set -- 5.6.3 Factorization of Poincaré Morphism for Toric Varieties -- 5.6.4 General Perversities -- 5.6.5 Equivariant Intersection Cohomology -- 5.6.6 Intersection Spaces. 5.6.7 Blown-Up Intersection Homology -- 5.6.8 Real Intersection Homology -- 5.6.9 Perverse Sheaves and Applications -- References -- 6 Milnor's Fibration Theorem for Real and Complex Singularities -- 6.1 Introduction -- 6.2 Exotic Spheres and the Birth of Milnor's Fibration -- 6.2.1 Singularities and Exotic Spheres -- 6.2.2 Open Questions -- 6.3 Model Example: the Brieskorn-Pham Singularities -- 6.3.1 Weighted Homogeneous Singularities -- 6.3.2 Real Analytic Singularities -- 6.4 Local Conical Structure of Analytic Sets -- 6.5 The Classical Fibration Theorems for Complex Singularities -- 6.6 Topology of the Link and the Fiber -- 6.6.1 The Link -- 6.6.2 The Fiber -- 6.6.3 Vanishing Cycles, Open-Books and the Monodromy -- 6.7 Extensions and Refinements of Milnor's Fibration Theorem -- 6.8 Milnor Fibration for Real Analytic Maps -- 6.8.1 Strong Milnor Condition -- 6.8.2 Model Singularities -- 6.9 On Functions with a Non-isolated Critical Point -- 6.9.1 Functions with an Isolated Critical Value -- 6.9.2 Polar Weighted Singularities -- 6.9.3 Functions with Arbitrary Discriminant -- 6.10 Milnor Fibrations and d-Regularity -- 6.10.1 The Case of an Isolated Critical Value -- 6.10.2 The General Case -- 6.11 Singularities of Mixed Functions -- References -- 7 Lê Cycles and Numbers of Hypersurface Singularities -- 7.1 Introduction and Earlier Results -- 7.2 Definitions and Basic Properties of Lê Cycles and Numbers -- 7.3 Lê Numbers and the Topology of the Milnor Fiber -- 7.4 Lê-Iomdine Formulas and Thom's Af Condition -- 7.5 Aligned Singularities and Hyperplane Arrangements -- 7.6 Other Characterizations of the Lê Cycles -- 7.7 Projective Lê Cycles -- References -- 8 Introduction to Mixed Hypersurface Singularity -- 8.1 A Quick Trip to the Complex Hypersurface Singularity Theory -- 8.1.1 Milnor Fibration -- 8.1.2 The Hamm-Lê lemma and a Tubular Milnor Fibration. 8.1.3 Weighted Homogeneous Polynomials -- 8.1.4 Newton Boundary and Non-degeneracy -- 8.2 Mixed Hypersurface Singularities -- 8.2.1 Mixed Analytic Functions -- 8.2.2 Mixed Singularities -- 8.2.3 A Tubular Milnor Fibration of a Real Analytic Mapping -- 8.2.4 Stratification and Thom's af-Regularity -- 8.3 Milnor Fibrations for Mixed Functions -- 8.3.1 Mixed Functions and Newton Boundary -- 8.3.2 Non-degeneracy of Mixed Functions -- 8.3.3 Mixed Functions of one Variable (n=1) -- 8.3.4 Mixed Weighted Homogeneous Polynomials -- 8.3.5 Milnor Fibrations for Strongly Non-degenerate Mixed Functions -- 8.3.6 The Milnor Fibration for Convenient Mixed Functions -- 8.3.7 The Spherical Milnor Fibration -- 8.3.8 Milnor Fibrations for Non-convenient Mixed Functions -- 8.3.9 Topological Stability -- 8.3.10 Equivalence of Tubular and Spherical Milnor Fibrations -- 8.3.11 Real Blowing Up and a Resolution of a Real Type -- 8.3.12 Simplicial Mixed Polynomials -- 8.3.13 The Join Theorem -- 8.3.14 Topology of the Milnor Fiber -- 8.3.15 The Milnor Fibration for fbarg -- 8.3.16 Mixed Projective Hypersurfaces -- 8.3.17 Remarks and Problems -- References -- 9 From Singularities to Polyhedral Products -- 9.1 Introduction -- 9.2 Singularity Theory -- 9.3 Dynamical Systems -- 9.3.1 Complex Differential Equations -- 9.3.2 Higher Dimensional Group Actions -- 9.3.3 Generalized Hopf Bifurcations -- 9.4 Geometry -- 9.4.1 Complex Geometry -- 9.4.2 Contact and Symplectic Geometry -- 9.5 To the Polyhedral Product Functor -- 9.5.1 Coxeter Groups, Small Covers and Toric Manifolds -- 9.5.2 The Polyhedral Product Functor -- 9.6 Back to Singularity Theory -- 9.6.1 Quadratic Cones -- 9.6.2 Singular Intersections and Smoothings -- References -- 10 Complements to Ample Divisors and Singularities -- 10.1 Introduction. 10.2 Braid Monodromy, Presentations of Fundamental Groups and Sufficient Conditions for Commutativity. |
| Record Nr. | UNINA-9910508474003321 |
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Handbook of geometry and topology of singularities III / / edited by José Luis Cisneros-Molina, Lê Dũng Tráng, and José Seade
| Handbook of geometry and topology of singularities III / / edited by José Luis Cisneros-Molina, Lê Dũng Tráng, and José Seade |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (822 pages) |
| Disciplina | 516.35 |
| Soggetto topico |
Singularities (Mathematics)
Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-95760-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996479368003316 |
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Handbook of geometry and topology of singularities III / / edited by José Luis Cisneros-Molina, Lê Dũng Tráng, and José Seade
| Handbook of geometry and topology of singularities III / / edited by José Luis Cisneros-Molina, Lê Dũng Tráng, and José Seade |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (822 pages) |
| Disciplina | 516.35 |
| Soggetto topico |
Singularities (Mathematics)
Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-95760-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910574864603321 |
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Handbook of Geometry and Topology of Singularities IV / / edited by José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade
| Handbook of Geometry and Topology of Singularities IV / / edited by José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade |
| Autore | Cisneros-Molina José Luis |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (622 pages) |
| Disciplina | 516.35 |
| Altri autori (Persone) |
Dũng TrángLê
SeadeJosé |
| Soggetto topico |
Topology
Algebraic geometry Mathematical analysis Algebraic Geometry Analysis Singularitats (Matemàtica) Geometria algebraica Grups topològics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-31925-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Lê Dũng Tráng and Bernard Teissier, Limits of tangents, Whitney stratifications and a Plücker type formula -- 2 Anne Frühbis-Krüger and Matthias Zach, Determinantal singularities -- 3 Shihoko Ishii, Singularities, the space of arcs and applications to birational geometry -- 4 Hussein Mourtada, Jet schemes and their applications in singularities, toric resolutions and integer partitions -- 5 Wolfgang Ebeling and Sabir M. Gusein-Zade, Indices of vector fields and 1-forms -- 6 Shoji Yokura, Motivic Hirzebruch class and related topics -- 7 Guillaume Valette, Regular vectors and bi-Lipschitz trivial stratifications in o-minimal structures -- 8 Lev Birbrair and Andrei Gabrielov, Lipschitz Geometry of Real Semialgebraic Surfaces -- 9 Alexandre Fernandes and José Edson Sampaio, Bi-Lipschitz invariance of the multiplicity -- 10 Lorenzo Fantini and Anne Pichon, On Lipschitz Normally Embedded singularities -- 11 Ana Bravo and Santiago Encinas, Hilbert-Samuel multiplicity and finite projections -- 12 Francisco J. Castro-Jiménez, David Mond and Luis Narváez-Macarro, Logarithmic Comparison Theorems. |
| Record Nr. | UNINA-9910747591903321 |
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Cisneros-Molina José Luis
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Normal surface singularities / / András Némethi
| Normal surface singularities / / András Némethi |
| Autore | Némethi András |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (732 pages) |
| Disciplina | 516.35 |
| Collana | Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics |
| Soggetto topico |
Singularities (Mathematics)
Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031067532
9783031067525 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996495170403316 |
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Némethi András
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Normal surface singularities / / András Némethi
| Normal surface singularities / / András Némethi |
| Autore | Némethi András |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (732 pages) |
| Disciplina | 516.35 |
| Collana | Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics |
| Soggetto topico |
Singularities (Mathematics)
Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031067532
9783031067525 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910616394003321 |
|
Némethi András
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Singularities and their interaction with geometry and low dimensional topology : in honor of András Némethi / / Javier Fernández de Bobadilla, Tamás László, András Stipsicz, editors
| Singularities and their interaction with geometry and low dimensional topology : in honor of András Némethi / / Javier Fernández de Bobadilla, Tamás László, András Stipsicz, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (341 pages) |
| Disciplina | 516.35 |
| Collana | Trends in Mathematics |
| Soggetto topico |
Singularities (Mathematics)
Singularitats (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-61958-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- The Scientific Life and Work of András Némethi -- Contents -- Versality, Bounds of Global Tjurina Numbers and Logarithmic Vector Fields Along Hypersurfaces with Isolated Singularities -- 1 Introduction -- 2 Versality of Hypersurfaces with Isolated Singularities -- 3 Bounds on the Global Tjurina Number, Stability and Torelli Properties -- References -- On Ideal Filtrations for Newton Nondegenerate Surface Singularities -- 1 Introduction -- 2 Associated Power Series and the Search for an Equation -- 3 Newton Nondegeneracy -- 4 The Intersection Lattice -- 5 Cycles, Newton Diagrams and the Cone -- 6 Equality Between Ideals -- 7 Suspension Singularities -- 8 An Example -- References -- Young Walls and Equivariant Hilbert Schemes of Points in Type D -- 1 Introduction -- 2 Young Walls of Type Dn -- 3 Abacus Combinatorics -- 4 Enumeration of Young Walls -- References -- Real Seifert Forms, Hodge Numbers and Blanchfield Pairings -- 1 Introduction -- 2 Milnor Fibration and Picard-Lefschetz Theory -- 3 Hermitian Variation Structures and Their Classification -- 3.1 Abstract Definition -- 3.2 Classification of HVS Over C -- 3.3 The Mod 2 Spectrum -- 4 HVS for Knots and Links -- 4.1 Three Results of Keef -- 4.2 HVS for Links and Classical Invariants -- 4.3 Signatures, HVS and Semicontinuity of the Spectrum -- 5 Blanchfield Forms -- 5.1 Definitions -- 5.2 Blanchfield Pairing Over R[t,t-1] -- 5.3 Variation Operators and Linking Forms -- 6 Twisted Blanchfield Forms and Applications -- 6.1 Construction of Twisted Pairings -- 6.2 Twisted Hodge Numbers and Twisted Signatures -- 6.3 A Few Words on Case F=C -- 6.4 A Closing Remark -- References -- ħ-Deformed Schubert Calculus in Equivariant Cohomology, K-Theory, and Elliptic Cohomology -- 1 Introduction -- 2 Ordinary and Equivariant Cohomological Schubert Calculus.
2.1 Schubert Classes and Structure Coefficients -- 3 The Main Theorem -- 4 The Partial Flag Variety -- 5 Elliptic Functions -- 5.1 Theta Functions -- 5.2 Fay's Trisecant Identity -- 6 Equivariant Elliptic Cohomology of Fλ -- 7 ħ-Deformed Schubert Classes in H*, K, and Ell -- 7.1 ħ-Deformed Schubert Class in Cohomology: CSM Class -- 7.2 ħ-Deformed Schubert Class in K Theory: Motivic Chern Class -- 7.3 ħ-Deformed Schubert Class in Elliptic Cohomology: The Elliptic Class -- 8 Weight Functions and Their Orthogonality Relations -- 8.1 Rational Weight Functions -- 8.2 Trigonometric Weight Functions -- 8.3 Elliptic Weight Functions -- 8.4 Orthogonality -- 8.5 Weight Functions Represent ħ-Deformed Schubert Classes -- 9 Sample Schubert Structure Constants -- 9.1 Cohomology -- 9.2 Equivariant Elliptic Cohomology -- 9.3 Non-equivariant Elliptic Cohomology -- 9.4 Positivity? -- References -- Fundamental Groups and Path Lifting for Algebraic Varieties -- 1 Introduction -- 2 Maps Between Fundamental Groups -- 3 Open and Universally Open Maps -- 4 Path Lifting in the Euclidean Topology -- 4.1 Examples -- References -- Cremona Transformations of Weighted Projective Planes, Zariski Pairs, and Rational Cuspidal Curves -- 1 Introduction -- 2 Quotient Singularities and Weighted Cremona Transformations -- 2.1 Curves in Quotient Surface Singularities -- 2.2 Weighted Projective Planes -- 2.3 Weighted Blow-ups -- 2.4 Weighted Cremona Transformations -- 3 Zariski Pairs on Weighted Projective Planes -- 3.1 Fundamental Groups of Complements -- 3.2 A Family of Zariski Pairs of Irreducible Weighted Projective Curves -- 3.3 Cyclic Covers and Their Irregularity à la Esnault-Viehweg -- 4 Some Rational Cuspidal Curves on Weighted Projective Planes -- 4.1 Rational Cuspidal Curves via Weighted Cremona Transformations -- 4.2 Rational Cuspidal Curves via Weighted Kummer Covers. 4.3 A rational Cuspidal Curve with Four Cusps -- 4.4 Milnor Fibers -- 5 Weighted Lê-Yomdin Surface Singularities -- 5.1 The Determinant of a Normal Surface Singularity -- 5.2 Superisolated and Lê-Yomdin Singularities -- 5.3 Weighted Lê-Yomdin Singularities -- 6 Normal Surface Singularities with Rational Homology Sphere Links -- 6.1 Brieskorn-Pham Singularities -- 6.2 Examples from Cremona and Kummer -- 6.3 Integral Homology Sphere Surface Singularities -- References -- Normal Reduction Numbers of Normal Surface Singularities -- 1 Introduction -- 2 Cycles and Cohomology -- 3 Cohomology and Normal Reduction Numbers -- 4 Cone-Like Singularities -- 4.1 Homogeneous Hypersurface Singularities -- 5 Brieskorn Complete Intersections -- 5.1 The Maximal Ideal Cycle, the Fundamental Cycle, and the Canonical Cycle -- 5.2 The Normal Reduction Numbers -- 5.3 Elliptic Singularities of Brieskorn Type -- References -- Motivic Chern Classes of Cones -- 1 Introduction -- 2 What Is the K-Class of a Subvariety? -- 2.1 Algebraic K-Theory and the Sheaf K-Class -- 2.2 Topological K-Theory -- 2.3 The K-Theory of Pn -- 2.4 Hilbert Polynomial -- 2.5 The Pushforward K-Class -- 2.6 Motivic Invariants and the Motivic K-Class -- 2.7 The Todd Genus -- 2.8 Genus of Smooth Hypersurfaces -- 2.9 The χy Genus -- 3 Cones -- 3.1 The Projective Case -- 4 Equivariant Classes -- 4.1 Universal Classes in K-Theory -- 4.2 Equivariant Classes of Cones in Cohomology: The Projective Thom Polynomial -- 4.3 Projective Thom Polynomial for the Motivic Chern Class -- 4.3.1 The Kirwan Map in K-Theory -- 4.3.2 The Affine to Projective Formula -- 4.4 The Projective to Affine Formula -- References -- Semicontinuity of Singularity Invariants in Families of Formal Power Series -- 1 Introduction -- 2 Quasi-Finite Modules and Semicontinuity -- 2.1 The Completed Tensor Product -- 2.2 Fibre and Completed Fibre. 2.3 Semicontinuity Over a 1-Dimensional Ring -- 2.4 Henselian Rings and Henselian Tensor Product -- 2.5 Semicontinuity for Algebraically Presented Modules -- 2.6 Related Results -- 3 Singularity Invariants -- 3.1 Isolated Singularities and Flatness -- 3.2 Milnor Number and Tjurina Number of Hypersurface Singularities -- 3.3 Determinacy of Ideals -- 3.4 Tjurina Number of Complete Intersection Singularities -- References -- Lattices and Correction Terms -- 1 Introduction -- 2 Lattices -- 3 Rational Homology Spheres and Correction Terms -- 4 Examples -- References -- Complex Surface Singularities with Rational HomologyDisk Smoothings -- 1 Introduction -- 2 Locations of -1 Curves -- 3 How to Find Sets of -1 Curves -- 4 Type Γ=W(p,q,r) -- 5 Type Γ=N(p,q,r), p> -- 0 -- 5.1 Case I for N(p,q,r), p> -- 0 -- 5.2 Case II for N(p,q,r), p> -- 0 -- 5.3 Case III for N(p,q,r), p> -- 0 -- 5.4 Type Γ=N(0,q,r) -- 6 Type Γ=M(p,q,r) -- 6.1 Case III for M(p,q,r), p,r> -- 0 -- 6.2 Case II for M(p,q,r), p,r> -- 0 -- 6.3 Case I for M(p,q,r), p,r> -- 0 -- 6.4 Type Γ=M(0,q,r), r ≥1 -- 6.5 Type Γ=M(p,q,0), p≥1 -- 6.6 Type Γ=M(0,q,0) -- 7 Self-Isotropic Subgroups and Fowler's Method -- 7.1 Fowler's Approach -- 7.2 Number of QHD Smoothing Components -- Appendix -- References -- On Tjurina Transform and Resolution of Determinantal Singularities -- 1 Introduction -- 2 Preliminaries -- 2.1 Determinantal Singularities -- 2.2 Transformations -- 3 Resolutions of the Model Determinantal Varieties -- 4 Transformations of General Determinantal Singularities -- 5 When Is the Tjurina Transform a Complete Intersection -- 6 Using Tjurina Transform to Resolve Hypersurface Singularities -- References -- On the Boundary of the Milnor Fiber -- 1 Introduction -- 2 From the Non-critical Level to the Special Fiber -- 3 The Case of Complex Surfaces. 3.1 A Glance on Némethi-Szilárd's Work for Surface Singularities -- 3.2 On the Work of Michel-Pichon-Weber -- 3.3 On the Work of Fernández de Bobadilla and Menegon -- 4 The Vanishing Zone -- 5 The Vanishing Boundary Homology -- 6 Concluding Remarks -- References. |
| Record Nr. | UNISA-996466405303316 |
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
