Algebraic Curves and Riemann Surfaces for Undergraduates [[electronic resource] ] : The Theory of the Donut / / by Anil Nerode, Noam Greenberg |
Autore | Nerode Anil <1932-> |
Edizione | [1st ed. 2022.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
Descrizione fisica | 1 online resource (456 pages) |
Disciplina | 515.93 |
Soggetto topico |
Algebraic geometry
Functions of complex variables Global analysis (Mathematics) Manifolds (Mathematics) Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Corbes algebraiques Geometria algebraica Superfícies de Riemann |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-031-11616-X |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout’s theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions. |
Record Nr. | UNISA-996508571503316 |
Nerode Anil <1932-> | ||
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Algebraic Curves and Riemann Surfaces for Undergraduates : The Theory of the Donut / / by Anil Nerode, Noam Greenberg |
Autore | Nerode Anil <1932-> |
Edizione | [1st ed. 2022.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
Descrizione fisica | 1 online resource (456 pages) |
Disciplina | 515.93 |
Soggetto topico |
Algebraic geometry
Functions of complex variables Global analysis (Mathematics) Manifolds (Mathematics) Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Corbes algebraiques Geometria algebraica Superfícies de Riemann |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-031-11616-X |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout’s theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions. |
Record Nr. | UNINA-9910644265203321 |
Nerode Anil <1932-> | ||
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebraic Curves and Surfaces : A History of Shapes / / Laurent Busé, Fabrizio Catanese, and Elisa Postinghel |
Autore | Busé Laurent |
Edizione | [First edition.] |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
Descrizione fisica | 1 online resource (220 pages) |
Disciplina | 516.35 |
Collana | SISSA Springer Series |
Soggetto topico |
Geometry, Algebraic
Geometria algebraica |
Soggetto genere / forma | Llibres electrònics |
ISBN |
9783031241512
9783031241505 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Preface -- Abridged History of the Theory of Curves and Surfaces -- Contents of the Volume -- Contents -- 1 The P12-Theorem: The Classification of Surfaces and Its Historical Development -- 1.1 Introduction -- 1.2 Lecture I: The Basic Set Up -- 1.2.1 First New Concepts Introduced by Enriques -- 1.2.1.1 Intersection Product -- 1.2.1.2 The Severi Group and the Neron-Severi Group -- 1.2.2 The Canonical Divisor and Riemann-Roch for Divisors on Surfaces -- 1.2.2.1 The Hurwitz Formula -- 1.2.3 The Arithmetic Genus of a Curve on a Surface -- 1.2.4 Linear Systems and Morphisms -- 1.2.5 Exceptional Curves of the First Kind and the Theorem of Castelnuovo-Enriques -- 1.2.6 Birational Invariants of S and the Albanese Variety -- 1.2.6.1 Irregular Surfaces and the Albanese Variety -- 1.2.7 Uniqueness Versus Non Uniqueness of Minimal Models -- 1.2.7.1 Elementary Transformations of Geometrically Ruled Surfaces -- 1.2.8 Castelnuovo's Key Theorem -- 1.2.9 Biregular Invariants of the Minimal Model -- 1.3 Lecture II: First Important Results for the Classification Theorem of Surfaces -- 1.3.1 A Basic Tool: Unramified Coverings -- 1.3.2 Castelnuovo's Theorem on Irregular Ruled Surfaces -- 1.3.3 Surfaces Fibred Over Curves -- 1.3.4 Castelnuovo's Criterion of Rationality -- 1.4 Lecture III: The Classification Theorem -- 1.4.1 Description of the Surfaces with 12 KS 0 (Case II, P12(S)=1) -- 1.4.2 Hyperelliptic Surfaces -- 1.5 Lecture IV: Isotriviality. Central Methods and Ideas in the Proof of the P12-Theorem -- 1.5.1 Structure of the Proof of the Classification Theorem -- 1.5.1.1 The Canonical Divisor Formula for Elliptic Fibrations -- 1.5.1.2 On the Existence of Elliptic Fibrations -- 1.5.1.3 P12 of Elliptic Fibrations -- 1.5.2 The Special Case KS nef, KS2=0, pg(S)=0, q(S)=1 and the Crucial Theorem.
1.5.3 First Transcendental Proof of Isotriviality for Fibre Genus g = 1. -- 1.5.3.1 All the Fibres Smooth of Genus g=1 -- 1.5.3.2 g=1 and there are multiple fibres. -- 1.5.4 Second Transcendental Proof of Isotriviality Using Teichmüller Space for Fibre Genus g ≥2 -- 1.5.5 Modern Proof of Isotriviality Using Variation of Hodge Structures, and the Theorems of Fujita and Arakelov -- 1.5.5.1 Fujita's and Arakelov's Theorems -- 1.5.6 Algebraic Approaches by Castelnuovo-Enriques, Bombieri-Mumford -- 1.5.6.1 Lemma of Enriques and Mumford mum1 -- 1.6 Appendix: Surfaces with Arithmetic Genus -1, Hyperelliptic Surfaces and Elliptic Surfaces According to Enriques -- 1.6.1 Analysis of Enriques' Argument -- 1.6.2 An Explicit Example of Surfaces of Type (2.0,0) -- 1.7 Some Exercises -- 1.7.1 Exercise 1 : Exceptional Curves of the First Kind -- 1.7.2 Exercise 2 : Fibred Surfaces with Fibre Genus g=0 -- 1.7.3 Exercise 3 : Minimal K3 Surfaces, Surfaces with KS 0 (KS is Trivial), q(S) = 0 -- 1.7.4 Exercise 4: Enriques' Construction of Enriques Surfaces -- 1.7.5 Exercise 5: Construction of Enriques Surfaces via a Reye Congruence -- References -- 2 Linear Systems of Hypersurfaces with Singularities and Beyond -- 2.1 Introduction -- 2.2 Plane Singular Curves -- 2.2.1 Polynomial Interpolation Problems -- 2.2.2 Geometric Formulation: Linear Systems with Multiple Base Points -- 2.2.3 Algebraic Formulation: Ideals of Powers of Linear Forms -- 2.2.4 Plane Curves -- 2.2.4.1 The Segre-Harbourne-Gimigliano-Hirschowitz Conjecture -- 2.2.4.2 A Conjecture by Nagata -- 2.2.5 Standard Cremona Involution -- 2.2.6 Historical Readings -- 2.2.6.1 Linear Systems of Plane Curves -- 2.2.6.2 Castelnuovo-Mumford Regularity -- 2.2.7 Further Readings -- 2.2.7.1 Birkhoff Interpolation -- 2.2.7.2 Classification of Surfaces and (-1)-Curves -- 2.2.8 Exercises -- 2.3 Nodal Hypersurfaces. 2.3.1 The Exceptional Cases of the Alexander-Hirschowitz Theorem -- 2.3.1.1 Quadrics in Pn -- 2.3.1.2 Quartics in Pn, with n≤4 -- 2.3.1.3 Cubics in P4 with Seven Nodes -- 2.3.2 Degeneration Techniques in the Proofs of Theorem 2.15 -- 2.3.2.1 Specialisation of Points: Horace Methods -- 2.3.2.2 Degenerations of the Space -- 2.3.3 Secant Varieties of Veronese Varieties -- 2.3.4 Further Readings -- 2.3.4.1 Waring's Problem for Polynomials -- 2.3.5 Historical Readings -- 2.3.5.1 Degenerations and Castelnuovo's Exact Sequences -- 2.3.6 Exercises -- 2.4 Results and Conjectures in Higher Dimension: Base Loci -- 2.4.1 Laface-Ugaglia Conjecture for P3 -- 2.4.2 The Toric Case: n+1 Points of Pn -- 2.4.2.1 A Combinatorial Trick -- 2.4.3 Linear Base Locus: The Case s≤n+2 -- 2.4.3.1 Connections to the Fröberg-Iarrobino Conjecture -- 2.4.4 Base Locus Rational Normal Curves Through n+3 points of Pn and Their Secant Varieties -- 2.4.4.1 Divisorial Joins -- 2.4.5 Base Locus Weyl Cycles Through n+4 Points of Pn,n=3,4 -- 2.4.6 Concluding Remarks -- 2.4.7 Further Readings -- 2.4.7.1 Compactifications of the Moduli Space of Rational Curves -- 2.4.8 Exercises -- 2.5 Birational Properties of Blow-Ups -- 2.5.1 Ampleness, Very Ampleness and l-Very Ampleness -- 2.5.2 Cones of Divisors -- 2.5.2.1 Nef Cones -- 2.5.2.2 Mori Dream Spaces, Effective and Movable Cones of Divisors and Their Mori Chamber Decomposition -- 2.5.3 Further Readings -- 2.5.3.1 Jet Ampleness of Line Bundles -- 2.5.3.2 Blow-Ups of Projective Spaces, Moduli Theory and Hilbert's 14th Problem -- 2.5.3.3 Classification of Mori Dream Space Blow-Ups of Products of Projective Spaces -- 2.5.4 Exercises -- References -- 3 Implicit Representations of Rational Curves and Surfaces -- 3.1 Introduction -- 3.2 Plane Rational Curve Parameterizations -- 3.2.1 The Classical Implicitization Method. 3.2.2 Syzygies of Curve Parameterizations -- 3.2.3 Matrix Representations of Curve Parameterizations -- 3.2.4 Intersection of Two Rational Curves -- 3.2.5 Singular Points -- 3.2.6 Exercises -- 3.3 Matrix Representations in Elimination Theory -- 3.3.1 Fitting Elimination Ideals -- 3.3.1.1 Elimination Ideals -- 3.3.1.2 Fitting Invariants and Elimination Matrices -- 3.3.2 Finite Fibers and Elimination Matrices -- 3.3.3 Koszul-Type Elimination Matrices -- 3.3.3.1 The Ideal of Inertia Forms -- 3.3.3.2 Upper Bound on the Regularity -- 3.3.3.3 Elimination Matrices -- 3.3.4 Hybrid Elimination Matrices -- 3.3.4.1 Sylvester Forms -- 3.3.4.2 Elimination Matrices -- 3.3.5 Exercises -- 3.4 Rational Curve Parameterizations -- 3.4.1 Syzygies and the Equations of the Graph -- 3.4.2 Fibers by Means of Matrix Representations -- 3.4.3 Using Quadratic Relations -- 3.4.3.1 Sylvester Forms -- 3.4.3.2 Matrix Representations by Means of Linear and Quadratic Relations -- 3.4.4 Application to Intersection Problems -- 3.4.4.1 Inversion of a Point -- 3.4.4.2 Intersection of Two Rational Curves -- 3.4.5 Exercises -- 3.5 Rational Hypersurface Parameterizations -- 3.5.1 The Degree of Parameterized Hypersurfaces -- 3.5.2 Graph and Blowup Algebras -- 3.5.2.1 The Rees Algebra -- 3.5.2.2 The Symmetric Algebra -- 3.5.2.3 Approximation Complexes -- 3.5.3 Matrix Representations of Hypersurface Parameterizations -- 3.5.4 Applications to Intersection Problems -- 3.5.5 Further Readings -- References. |
Record Nr. | UNINA-9910720071903321 |
Busé Laurent | ||
Cham, Switzerland : , : Springer, , [2023] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
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Algebraic geometry and commutative algebra / / Siegfried Bosch |
Autore | Bosch S (Siegfried), <1944-> |
Edizione | [Second edition.] |
Pubbl/distr/stampa | London, England : , : Springer-Verlag, , [2022] |
Descrizione fisica | 1 online resource (508 pages) |
Disciplina | 516.35 |
Collana | Universitext |
Soggetto topico |
Geometry, Algebraic
Commutative algebra Algebra Geometria algebraica Àlgebra commutativa |
Soggetto genere / forma | Llibres electrònics |
ISBN |
9781447175230
9781447175223 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISA-996472037103316 |
Bosch S (Siegfried), <1944-> | ||
London, England : , : Springer-Verlag, , [2022] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Algebraic geometry and commutative algebra / / Siegfried Bosch |
Autore | Bosch S (Siegfried), <1944-> |
Edizione | [Second edition.] |
Pubbl/distr/stampa | London, England : , : Springer-Verlag, , [2022] |
Descrizione fisica | 1 online resource (508 pages) |
Disciplina | 516.35 |
Collana | Universitext |
Soggetto topico |
Geometry, Algebraic
Commutative algebra Algebra Geometria algebraica Àlgebra commutativa |
Soggetto genere / forma | Llibres electrònics |
ISBN |
9781447175230
9781447175223 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNINA-9910564691103321 |
Bosch S (Siegfried), <1944-> | ||
London, England : , : Springer-Verlag, , [2022] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebraic geometry between tradition and future : an Italian perspective / / edited by Gilberto Bini |
Edizione | [1st ed. 2023.] |
Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore Pte Ltd., , [2023] |
Descrizione fisica | 1 online resource (371 pages) |
Disciplina | 516.35 |
Collana | Springer INdAM Series |
Soggetto topico |
Geometry, Algebraic - History - 19th century
Geometry, Algebraic - History - 20th century Geometria algebraica Història de la matemàtica |
Soggetto genere / forma | Llibres electrònics |
ISBN |
9789811982811
9789811982804 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Gilberto Bini (Palermo), Introduction -- 2. Claudio Fontanari (Trento), Stefano Gattei (Trento), Francesco Severi’s Mathematical Library -- 3. Angelo Guerraggio (Milano), Francesco Severi and the Fascist Regime -- 4. Maria Giulia Lugaresi (Ferrara), Fabio Conforto (1909-1954).His Scientific and Academic Career at the University of Rome -- 5. Livia Giacardi (Torino), Alessandro Terracini (1889-1968). Teaching and Research from the University Years to the Racial Laws -- 6. Marco Andreatta (Trento), Higher Dimensional Geometry from Fano to Mori and Beyond -- 7. Livia Giacardi (Torino), Erika Luciano (Torino), Elena Scalambro(Torino), Gino Fano (1871-1952). The scientific Trajectory of an Italian Geometer between Internationalism and Persecution -- 8. Alessandro Verra (Roma), From Enriques Surface to Artin-Mumford Counterexample -- 9. Ciro Ciliberto (Roma), The Theorem of Completeness the Characteristic Series: Enriques' Contribution -- 10. Edoardo Sernesi (Roma), Severi, Zappa and the Characteristic System -- 11. Ciro Ciliberto (Roma), Claudio Fontanari (Trento). Two letters by Guido Castelnuovo -- 12. Claudio Fontanari (Trento), Guido Castelnuovo and his Heritage: Geometry, Combinatorics, Teaching -- 13. Enrico Rogora (Roma), Guido Castelnuovo (1865-1952) -- 14. Nicla Palladino (Perugia), Maria Alessandra Vaccaro (Palermo), The Genesis of the Italian School of Algebraic Geometry through the Correspondence between Luigi Cremona and Some of his Students -- 15. Aldo Brigaglia (Palermo), Veronese, Cremona and the Mystical Hexagram. |
Record Nr. | UNINA-9910720093503321 |
Singapore : , : Springer Nature Singapore Pte Ltd., , [2023] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Arakelov geometry and diophantine applications / / Emmanuel Peyre, Gaël Rémond, editors |
Edizione | [1st ed. 2021.] |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
Descrizione fisica | 1 online resource (X, 469 p.) |
Disciplina | 516.35 |
Collana | Lecture Notes in Mathematics |
Soggetto topico |
Arakelov theory
Geometria algebraica |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-030-57559-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISA-996466562803316 |
Cham, Switzerland : , : Springer, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Arakelov geometry and diophantine applications / / Emmanuel Peyre, Gaël Rémond, editors |
Edizione | [1st ed. 2021.] |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
Descrizione fisica | 1 online resource (X, 469 p.) |
Disciplina | 516.35 |
Collana | Lecture Notes in Mathematics |
Soggetto topico |
Arakelov theory
Geometria algebraica |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-030-57559-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNINA-9910484306503321 |
Cham, Switzerland : , : Springer, , [2021] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
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The art of doing algebraic geometry / / edited by Thomas Dedieu [and four others] |
Edizione | [1st ed. 2023.] |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
Descrizione fisica | 1 online resource (X, 424 p. 64 illus., 46 illus. in color.) |
Disciplina | 304.2 |
Collana | Trends in Mathematics |
Soggetto topico |
Geometry, Algebraic
Geometria algebraica |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-031-11938-X |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | M. C. Brambilla, O. Dumitrescu, E. Postinghel, “Weyl cycles on the blow-up of $P^4$ at eight points" -- A. Brigaglia, “Simson’s reconstruction of Apollonius’ Loci Plani. Modern ideas in classical language” -- F. Catanese, “Kummer quartic surfaces, strict self-duality, and more” -- L. Chiantini e Giorgio Ottaviani, “A footnote to a footnote to a paper of B. Segre” -- T. Dedieu and E. Sernesi, “Deformations and extensions of Gorenstein weighted projective spaces” -- V. Di Gennaro and Davide Franco, “Intersection cohomology and Severi Varieties” -- O. Dumitrescu and R. Miranda, “Cremona Orbits in $\mathbb P^4$ and Applications” -- F. Flamini and P. Supino, “On some components of Hilbert schemes of curves” -- Gerard van der Geer, “Siegel modular forms of degree two and three and invariant theory” -- A. Laface and L. Ugaglia, “On intrinsic negative curves” -- Angelo F. Lopez, with an appendix by Thomas Dedieu, “On the extendibility of projective varieties: a survey” -- M. Mella, “The minimal Cremona degree of quartic surfaces” -- M. Mendes Lopes and R. Pardini, “On the degree of the canonical map of a surface of general type” -- C. Pedrini, “Hyperkæhler varieties with a motive of abelian type” -- F. Polizzi and P. Sabatino, “Finite quotients of surface braid groups and double Kodaira fibrations” -- Y. Prokhorov and M. Zaidenberg, “Affine cones over Fano-Mukai fourfolds of genus 10 are flexible” -- J. Roé, “Enriques diagrams under pullback by a double cover” -- E. Rogora, “The “projective spirit” in Segre’s lectures on differential equations”. . |
Record Nr. | UNINA-9910767519903321 |
Cham, Switzerland : , : Springer, , [2023] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Basic Algebraic Geometry 1 : Varieties in Projective Space / / by Igor R. Shafarevich |
Autore | Shafarevich Igor R |
Edizione | [3rd ed. 2013.] |
Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013 |
Descrizione fisica | 1 online resource (326 p.) |
Disciplina | 516.35 |
Soggetto topico |
Algebraic geometry
Mathematical physics Geometria algebraica Algebraic Geometry Theoretical, Mathematical and Computational Physics |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-642-37956-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Preface -- Book 1. Varieties in Projective Space: Chapter 1. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index. |
Record Nr. | UNINA-9910438034203321 |
Shafarevich Igor R | ||
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2013 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
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