Progress in commutative algebra 1, combinatorics and homology /
Progress in commutative algebra 1, combinatorics and homology /
Combinatorics and homology
edited by Sean Sather-Wagstaff ... [and others].
- 1 online resource : illustrations.
- De Gruyter Proceedings in Mathematics .
- Gruyter Proceedings in Mathematics. .
2.2 Gabber's Proof of the Nonnegativity Conjecture.
Includes bibliographical references and index.
Preface; Boij-Sèoderberg Theory: Introduction and Survey; 1 The Boij-Sèoderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 Herzog-Kèuhl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The Boij-Sèoderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the Boij-Sèoderberg Fan and Their Supporting Hyperplanes; 2.1 The Exterior Facets; 2.2 The Supporting Hyperplanes; 2.3 Pairings of Vector Bundles and Resolutions. 3 The Existence of Pure Free Resolutions and of Vector Bundles with Supernatural Cohomology3.1 The Equivariant Pure Free Resolution; 3.2 Equivariant Supernatural Bundles; 3.3 Characteristic Free Supernatural Bundles; 3.4 The Characteristic Free Pure Resolutions; 3.5 Pure Resolutions Constructed from Generic Matrices; 4 Cohomology of Vector Bundles on Projective Spaces; 4.1 Cohomology Tables; 4.2 The Fan of Cohomology Tables of Vector Bundles; 4.3 Facet Equations; 5 Extensions to Non-Cohen-Macaulay Modules and to Coherent Sheaves; 5.1 Betti Diagrams of Graded Modules in General. 5.2 Cohomology of Coherent Sheaves6 Further Topics; 6.1 The Semigroup of Betti Diagrams of Modules; 6.2 Variations on the Grading; 6.3 Poset Structures; 6.4 Computer Packages; 6.5 Three Basic Problems; Hilbert Functions of Fat Point Subschemes of the Plane: the Two-fold Way; 1 Introduction; 2 Approach I: Nine Double Points; 3 Approach I: Points on Cubics; 4 Approach II: Points on Cubics; Edge Ideals: Algebraic and Combinatorial Properties; 1 Introduction; 2 Algebraic and Combinatorial Properties of Edge Ideals; 3 Invariants of Edge Ideals: Regularity, Projective Dimension, Depth. 4 Stability of Associated PrimesThree Simplicial Resolutions; 1 Introduction; 2 Background and Notation; 2.1 Algebra; 2.2 Combinatorics; 3 The Taylor Resolution; 4 Simplicial Resolutions; 5 The Scarf Complex; 6 The Lyubeznik Resolutions; 7 Intersections; 8 Questions; A Minimal Poset Resolution of Stable Ideals; 1 Introduction; 2 Poset Resolutions and Stable Ideals; 3 The Shellability of PN; 4 The topology of PN and properties of D (PN); 5 Proof of Theorem 2.4; 6 A Minimal Cellular Resolution of R/N; Subsets of Complete Intersections and the EGH Conjecture; 1 Introduction. 2 Preliminary Definitions and Results2.1 The Eisenbud-Green-Harris Conjecture and Complete Intersections; 2.2 Some Enumeration; 3 Rectangular Complete Intersections; 4 Some Key Tools; 4.1 Pairs of Hilbert Functions and Maximal Growth; 4.2 Ideals Containing Regular Sequences; 5 Subsets of Complete Intersections in P2; 6 Subsets of C.I. (2, d2,d3) with d2 = d3; 7 Subsets of C.I. (3, d2, d3) with d3 = d2; 8 An Application: The Cayley-Bacharach Property; The Homological Conjectures; 1 Introduction; 2 The Serre Multiplicity Conjectures; 2.1 The Vanishing Conjecture.
This is the first of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University meeting. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the lo.
9783110250404 (electronic bk.) 3110250403 (electronic bk.)
Commutative algebra.
Algebra.
Commutative algebra.
Mathematics.
MATHEMATICS / Algebra / Intermediate
Electronic books.
512
2.2 Gabber's Proof of the Nonnegativity Conjecture.
Includes bibliographical references and index.
Preface; Boij-Sèoderberg Theory: Introduction and Survey; 1 The Boij-Sèoderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 Herzog-Kèuhl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The Boij-Sèoderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the Boij-Sèoderberg Fan and Their Supporting Hyperplanes; 2.1 The Exterior Facets; 2.2 The Supporting Hyperplanes; 2.3 Pairings of Vector Bundles and Resolutions. 3 The Existence of Pure Free Resolutions and of Vector Bundles with Supernatural Cohomology3.1 The Equivariant Pure Free Resolution; 3.2 Equivariant Supernatural Bundles; 3.3 Characteristic Free Supernatural Bundles; 3.4 The Characteristic Free Pure Resolutions; 3.5 Pure Resolutions Constructed from Generic Matrices; 4 Cohomology of Vector Bundles on Projective Spaces; 4.1 Cohomology Tables; 4.2 The Fan of Cohomology Tables of Vector Bundles; 4.3 Facet Equations; 5 Extensions to Non-Cohen-Macaulay Modules and to Coherent Sheaves; 5.1 Betti Diagrams of Graded Modules in General. 5.2 Cohomology of Coherent Sheaves6 Further Topics; 6.1 The Semigroup of Betti Diagrams of Modules; 6.2 Variations on the Grading; 6.3 Poset Structures; 6.4 Computer Packages; 6.5 Three Basic Problems; Hilbert Functions of Fat Point Subschemes of the Plane: the Two-fold Way; 1 Introduction; 2 Approach I: Nine Double Points; 3 Approach I: Points on Cubics; 4 Approach II: Points on Cubics; Edge Ideals: Algebraic and Combinatorial Properties; 1 Introduction; 2 Algebraic and Combinatorial Properties of Edge Ideals; 3 Invariants of Edge Ideals: Regularity, Projective Dimension, Depth. 4 Stability of Associated PrimesThree Simplicial Resolutions; 1 Introduction; 2 Background and Notation; 2.1 Algebra; 2.2 Combinatorics; 3 The Taylor Resolution; 4 Simplicial Resolutions; 5 The Scarf Complex; 6 The Lyubeznik Resolutions; 7 Intersections; 8 Questions; A Minimal Poset Resolution of Stable Ideals; 1 Introduction; 2 Poset Resolutions and Stable Ideals; 3 The Shellability of PN; 4 The topology of PN and properties of D (PN); 5 Proof of Theorem 2.4; 6 A Minimal Cellular Resolution of R/N; Subsets of Complete Intersections and the EGH Conjecture; 1 Introduction. 2 Preliminary Definitions and Results2.1 The Eisenbud-Green-Harris Conjecture and Complete Intersections; 2.2 Some Enumeration; 3 Rectangular Complete Intersections; 4 Some Key Tools; 4.1 Pairs of Hilbert Functions and Maximal Growth; 4.2 Ideals Containing Regular Sequences; 5 Subsets of Complete Intersections in P2; 6 Subsets of C.I. (2, d2,d3) with d2 = d3; 7 Subsets of C.I. (3, d2, d3) with d3 = d2; 8 An Application: The Cayley-Bacharach Property; The Homological Conjectures; 1 Introduction; 2 The Serre Multiplicity Conjectures; 2.1 The Vanishing Conjecture.
This is the first of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University meeting. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the lo.
9783110250404 (electronic bk.) 3110250403 (electronic bk.)
Commutative algebra.
Algebra.
Commutative algebra.
Mathematics.
MATHEMATICS / Algebra / Intermediate
Electronic books.
512