Progress in Commutative Algebra 1
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Progress in Commutative Algebra 1: Combinatorics and Homology

Progress in Commutative Algebra 1: Combinatorics and Homology

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About the Book

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 local theory, graded situation and its interactions with combinatorics and geometry). This fist volume concentrates on combinatorics and homology.

Table of Contents:
Preface; 1 Boij-Soederberg Theory: Introduction and Survey Gunnar Floystad; 1.1 Introduction; 1.2 The Boij-Soderberg Conjectures; 1.2.1 Resolutions and Betti Diagrams; 1.2.2 The Positive Cone of Betti Diagrams; 1.2.3 Herzog-Kuhl Equations; 1.2.4 Pure Resolutions; 1.2.5 Linear Combinations of Pure Diagrams; 1.2.6 The Boij-Soderberg Conjectures; 1.2.7 Algorithmic Interpretation; 1.2.8 Geometric Interpretation; 1.3 The Exterior Facets of the Boij-Soderberg Fan and their Supporting Hyperplanes; 1.3.1 The Exterior Facets; 1.3.2 The Supporting Hyperplanes; 1.3.3 Pairings of vector Bundles and Resolutions; 1.4 The Existence of Pure Free Resolutions and of Vector Bundles with Supernatural Cohomology; 1.4.1 The Equivariant Pure Free Resolution; 1.4.2 Equivariant Supernatural Bundles; 1.4.3 Characteristic Free Supernatural Bundles; 1.4.4 The Characteristic Free Pure Resolution; 1.4.5 Pure Resolutions Constructed from Generic Matrices; 1.5 Cohomology of Vector Bundles on Projective Spaces; 1.5.1 Cohomology Tables; 1.5.2 The Fan of Cohomology Tables of Vector Bundles; 1.5.3 Facet Equations; 1.6 Extensions to Non-Cohen-Macaulay Modules and to Coherent Sheaves; 1.6.1 Betti Diagrams of Graded Modules in General; 1.6.2 Cohomology of Coherent Sheaves; 1.7 Further Topics; 1.7.1 The Semigroup of Betti Diagrams of Modules; 1.7.2 Variants on the Grading; 1.7.3 Poset Structures; 1.7.4 Computer Packages; 1.7.5 Three Basic.


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Product Details
  • ISBN-13: 9783112190203
  • Publisher: De Gruyter
  • Binding: SA
  • Language: English
  • Returnable: N
  • Width: 170 mm
  • ISBN-10: 3112190203
  • Publisher Date: 26 Apr 2012
  • Height: 240 mm
  • No of Pages: 361
  • Sub Title: Combinatorics and Homology


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Progress in Commutative Algebra 1: Combinatorics and Homology
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