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The Resource Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean SatherWagstaff [and others], (electronic resource)
Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean SatherWagstaff [and others], (electronic resource)
Resource Information
The item Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean SatherWagstaff [and others], (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Progress in commutative algebra, 1, Combinatorics and homology, edited by Sean SatherWagstaff [and others], (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Contributor

 Fløystad, Gunnar
 ebrary
 Geramita, A. V
 Cooper, Susan M
 Vassilev, Janet C
 Harbourne, Brian
 Cooper, Susan M
 Migliore, Juan C
 Villarreal Rodríguez, Rafael Heraclio
 Francisco, Christopher
 Geramita, A. V
 Mermin, Jeff
 Clark, Timothy B. P
 SatherWagstaff, Sean
 Hummel, Livia
 Roberts, Paul C
 Klingler, Lee C
 Leuschke, Graham J
 Fløystad, Gunnar
 Yao, Yongwei
 Morey, Susan
 Francisco, Christopher
 SatherWagstaff, Sean
 Summary
 This is the first of two volumes of a stateoftheart 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 nonNoetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: nonnoetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the lo
 Language
 eng
 Extent
 1 online resource
 Note
 2.2 Gabber's Proof of the Nonnegativity Conjecture
 Contents

 Preface; BoijSöderberg Theory: Introduction and Survey; 1 The BoijSöderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 HerzogKühl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The BoijSöderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the BoijSöderberg 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 NonCohenMacaulay 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 Twofold 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 EisenbudGreenHarris 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 CayleyBacharach Property; The Homological Conjectures; 1 Introduction; 2 The Serre Multiplicity Conjectures; 2.1 The Vanishing Conjecture
 Isbn
 9783112190203
 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 SatherWagstaff [and others]
 Title variation
 Combinatorics and homology
 Contributor

 Fløystad, Gunnar
 ebrary
 Geramita, A. V
 Cooper, Susan M
 Vassilev, Janet C
 Harbourne, Brian
 Cooper, Susan M
 Migliore, Juan C
 Villarreal Rodríguez, Rafael Heraclio
 Francisco, Christopher
 Geramita, A. V
 Mermin, Jeff
 Clark, Timothy B. P
 SatherWagstaff, Sean
 Hummel, Livia
 Roberts, Paul C
 Klingler, Lee C
 Leuschke, Graham J
 Fløystad, Gunnar
 Yao, Yongwei
 Morey, Susan
 Francisco, Christopher
 SatherWagstaff, Sean
 Language
 eng
 Summary
 This is the first of two volumes of a stateoftheart 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 nonNoetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: nonnoetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the lo
 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
 SatherWagstaff, 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 SatherWagstaff [and others], (electronic resource)
 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; BoijSöderberg Theory: Introduction and Survey; 1 The BoijSöderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 HerzogKühl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The BoijSöderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the BoijSöderberg 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 NonCohenMacaulay 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 Twofold 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 EisenbudGreenHarris 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 CayleyBacharach 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 SatherWagstaff [and others], (electronic resource)
 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; BoijSöderberg Theory: Introduction and Survey; 1 The BoijSöderberg Conjectures; 1.1 Resolutions and Betti Diagrams; 1.2 The Positive Cone of Betti Diagrams; 1.3 HerzogKühl Equations; 1.4 Pure resolutions; 1.5 Linear Combinations of Pure Diagrams; 1.6 The BoijSöderberg Conjectures; 1.7 Algorithmic Interpretation; 1.8 Geometric Interpretation; 2 The Exterior Facets of the BoijSöderberg 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 NonCohenMacaulay 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 Twofold 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 EisenbudGreenHarris 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 CayleyBacharach 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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