The Resource Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean Sather-Wagstaff [and others], (electronic resource)

Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean Sather-Wagstaff [and others], (electronic resource)

Label
Progress in commutative algebra, 1, Combinatorics and homology
Title
Progress in commutative algebra
Title number
1
Title part
Combinatorics and homology
Statement of responsibility
edited by Sean Sather-Wagstaff [and others]
Title variation
Combinatorics and homology
Contributor
Provider
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
EBLCP
Illustrations
illustrations
Index
no index present
LC call number
QA251.3
LC item number
.P76 2012eb
Literary form
non fiction
Nature of contents
  • standards specifications
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • ebrary
  • Sather-Wagstaff, Sean
  • Villarreal Rodríguez, Rafael Heraclio
  • Yao, Yongwei
  • Fløystad, Gunnar
  • Mermin, Jeff
  • Geramita, A. V
  • Roberts, Paul C
  • Morey, Susan
  • Vassilev, Janet C
  • Francisco, Christopher
  • Clark, Timothy B. P
  • Hummel, Livia
  • Klingler, Lee C
  • Harbourne, Brian
  • Cooper, Susan M
  • Leuschke, Graham J
  • Migliore, Juan C
http://library.link/vocab/subjectName
  • Commutative algebra
  • Algebra
  • Mathematics
  • MATHEMATICS
  • Commutative algebra
Label
Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean Sather-Wagstaff [and others], (electronic resource)
Instantiates
Publication
Note
2.2 Gabber's Proof of the Nonnegativity Conjecture
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface; Boij-Söderberg Theory: Introduction and Survey; 1 The Boij-Söderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 Herzog-Kühl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The Boij-Söderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the Boij-Söderberg 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
Dimensions
unknown
Extent
1 online resource
Form of item
electronic
Isbn
9783112190203
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
illustrations.
Specific material designation
remote
System control number
  • (OCoLC)795120008
  • (OCoLC)ocn795120008
Label
Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean Sather-Wagstaff [and others], (electronic resource)
Publication
Note
2.2 Gabber's Proof of the Nonnegativity Conjecture
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface; Boij-Söderberg Theory: Introduction and Survey; 1 The Boij-Söderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 Herzog-Kühl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The Boij-Söderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the Boij-Söderberg 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
Dimensions
unknown
Extent
1 online resource
Form of item
electronic
Isbn
9783112190203
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
illustrations.
Specific material designation
remote
System control number
  • (OCoLC)795120008
  • (OCoLC)ocn795120008

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