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Minimal Free Resolutions over Complete Intersections [[electronic resource] /] / by David Eisenbud, Irena Peeva
| Minimal Free Resolutions over Complete Intersections [[electronic resource] /] / by David Eisenbud, Irena Peeva |
| Autore | Eisenbud David |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (X, 107 p.) |
| Disciplina | 512.62 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Commutative algebra
Commutative rings Algebraic geometry Category theory (Mathematics) Homological algebra Mathematical physics Commutative Rings and Algebras Algebraic Geometry Category Theory, Homological Algebra Theoretical, Mathematical and Computational Physics |
| ISBN | 3-319-26437-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Acknowledgments -- Contents -- 1 Introduction and Survey -- 1.1 How We Got Here -- Revealing the Pattern -- 1.2 What is a Higher Matrix Factorization? -- Matrix Factorizations of a Sequence of Elements -- 1.3 What's in This Book? -- High Syzygies are Higher Matrix Factorization Modules -- Minimal R-Free and S-Free Resolutions -- Syzygies over Intermediate Quotient Rings -- 1.4 Notation and Conventions -- 2 Matrix Factorizations of One Element -- 2.1 Matrix Factorizations and Resolutions over a Hypersurface -- 3 Finite Resolutions of HMF Modules -- 3.1 The Minimal S-Free Resolution of a Higher Matrix Factorization Module -- 3.2 Consequences -- 3.3 Building a Koszul Extension -- 3.4 Higher Homotopies -- 4 CI Operators -- 4.1 CI Operators -- 4.2 The Action of the CI Operators on Ext -- 4.3 Resolutions with a Surjective CI Operator -- 5 Infinite Resolutions of HMF Modules -- 5.1 The Minimal R-Free Resolution of a Higher Matrix Factorization Module -- 5.2 Betti Numbers -- 5.3 Strong Matrix Factorizations -- 5.4 Resolutions over Intermediate Rings -- 6 Far-Out Syzygies -- 6.1 Pre-stable Syzygies and Generic CI Operators -- 6.2 The Graded Case -- 6.3 The Box Complex -- 6.4 From Syzygies to Higher Matrix Factorizations -- 6.5 Betti Numbers of Pre-stable Matrix Factorizations -- 7 The Gorenstein Case -- 7.1 Syzygies and Maximal Cohen-Macaulay Modules -- 7.2 Stable Syzygies in the Gorenstein Case -- 7.3 Maximal Cohen-Macaulay Approximations -- 7.4 Stable Matrix Factorizations over a Gorenstein Ring -- 8 Functoriality -- 8.1 HMF Morphisms -- References -- Index. |
| Record Nr. | UNINA-9910136809303321 |
Eisenbud David
|
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Minimal Free Resolutions over Complete Intersections [[electronic resource] /] / by David Eisenbud, Irena Peeva
| Minimal Free Resolutions over Complete Intersections [[electronic resource] /] / by David Eisenbud, Irena Peeva |
| Autore | Eisenbud David |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (X, 107 p.) |
| Disciplina | 512.62 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Commutative algebra
Commutative rings Algebraic geometry Category theory (Mathematics) Homological algebra Mathematical physics Commutative Rings and Algebras Algebraic Geometry Category Theory, Homological Algebra Theoretical, Mathematical and Computational Physics |
| ISBN | 3-319-26437-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Acknowledgments -- Contents -- 1 Introduction and Survey -- 1.1 How We Got Here -- Revealing the Pattern -- 1.2 What is a Higher Matrix Factorization? -- Matrix Factorizations of a Sequence of Elements -- 1.3 What's in This Book? -- High Syzygies are Higher Matrix Factorization Modules -- Minimal R-Free and S-Free Resolutions -- Syzygies over Intermediate Quotient Rings -- 1.4 Notation and Conventions -- 2 Matrix Factorizations of One Element -- 2.1 Matrix Factorizations and Resolutions over a Hypersurface -- 3 Finite Resolutions of HMF Modules -- 3.1 The Minimal S-Free Resolution of a Higher Matrix Factorization Module -- 3.2 Consequences -- 3.3 Building a Koszul Extension -- 3.4 Higher Homotopies -- 4 CI Operators -- 4.1 CI Operators -- 4.2 The Action of the CI Operators on Ext -- 4.3 Resolutions with a Surjective CI Operator -- 5 Infinite Resolutions of HMF Modules -- 5.1 The Minimal R-Free Resolution of a Higher Matrix Factorization Module -- 5.2 Betti Numbers -- 5.3 Strong Matrix Factorizations -- 5.4 Resolutions over Intermediate Rings -- 6 Far-Out Syzygies -- 6.1 Pre-stable Syzygies and Generic CI Operators -- 6.2 The Graded Case -- 6.3 The Box Complex -- 6.4 From Syzygies to Higher Matrix Factorizations -- 6.5 Betti Numbers of Pre-stable Matrix Factorizations -- 7 The Gorenstein Case -- 7.1 Syzygies and Maximal Cohen-Macaulay Modules -- 7.2 Stable Syzygies in the Gorenstein Case -- 7.3 Maximal Cohen-Macaulay Approximations -- 7.4 Stable Matrix Factorizations over a Gorenstein Ring -- 8 Functoriality -- 8.1 HMF Morphisms -- References -- Index. |
| Record Nr. | UNISA-996466760603316 |
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Eisenbud David
|
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 / / David Eisenbud, Walter D. Neumann
| Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 / / David Eisenbud, Walter D. Neumann |
| Autore | Eisenbud David |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (184 pages) : illustration |
| Disciplina | 514.2 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Link theory
Invariants Curves, Plane Singularities (Mathematics) |
| Soggetto non controllato |
3-sphere
Alexander Grothendieck Alexander polynomial Algebraic curve Algebraic equation Algebraic geometry Algebraic surface Algorithm Ambient space Analytic function Approximation Big O notation Call graph Cartesian coordinate system Characteristic polynomial Closed-form expression Cohomology Computation Conjecture Connected sum Contradiction Coprime integers Corollary Curve Cyclic group Determinant Diagram (category theory) Diffeomorphism Dimension Disjoint union Eigenvalues and eigenvectors Equation Equivalence class Euler number Existential quantification Exterior (topology) Fiber bundle Fibration Foliation Fundamental group Geometry Graph (discrete mathematics) Ground field Homeomorphism Homology sphere Identity matrix Integer matrix Intersection form (4-manifold) Isolated point Isolated singularity Jordan normal form Knot theory Mathematical induction Monodromy matrix Monodromy N-sphere Natural transformation Newton polygon Newton's method Normal (geometry) Notation Pairwise Parametrization Plane curve Polynomial Power series Projective plane Puiseux series Quantity Rational function Resolution of singularities Riemann sphere Riemann surface Root of unity Scientific notation Seifert surface Set (mathematics) Sign (mathematics) Solid torus Special case Stereographic projection Submanifold Summation Theorem Three-dimensional space (mathematics) Topology Torus knot Torus Tubular neighborhood Unit circle Unit vector Unknot Variable (mathematics) |
| ISBN | 1-4008-8192-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Abstract -- Three-Dimensional Link Theory and Invariants of Plane Curve Singularities -- Introduction -- Review -- Preview -- Chapter I: Foundations -- Appendix to Chapter I: Algebraic Links -- Chapter II: Classification -- Chapter III: Invariants -- Chapter IV: Examples -- Chapter V: Relation to Plumbing -- References -- Backmatter |
| Record Nr. | UNINA-9910154742903321 |
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Eisenbud David
|
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| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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