Commutative Algebra

Table of Contents

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   Book Overview
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   Chapter 1 Lazarsfeld–Mukai Bundles and Applications
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   Chapter 2 Some Applications of Commutative Algebra to String Theory
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   Chapter 3 Commutative Algebra
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   Chapter 4 Three Flavors of Extremal Betti Tables
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   Chapter 5 p −1-Linear Maps in Algebra and Geometry
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   Chapter 6 Castelnuovo–Mumford Regularity of Annihilators, Ext and Tor Modules
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   Chapter 7 Selections from the Letter-Place Panoply
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   Chapter 8 Koszul Algebras and Regularity
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    Chapter 9 Powers of Ideals: Betti Numbers, Cohomology and Regularity
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    Chapter 10 Some Homological Properties of Modules over a Complete Intersection, with Applications
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    Chapter 11 Powers of Square-Free Monomial Ideals and Combinatorics
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    Chapter 12 A Brief History of Order Ideals
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    Chapter 13 Moduli of Abelian Varieties, Vinberg θ-Groups, and Free Resolutions
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    Chapter 14 F-Purity, Frobenius Splitting, and Tight Closure
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    Chapter 15 Hilbert–Kunz Multiplicity and the F-Signature
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    Chapter 16 Pure O-Sequences: Known Results, Applications, and Open Problems
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    Chapter 17 Bounding Projective Dimension
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    Chapter 18 Brauer–Thrall Theory for Maximal Cohen–Macaulay Modules
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    Chapter 19 Tight Closure’s Failure to Localize - a Self-Contained Exposition
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    Chapter 20 Introduction to the Hyperdeterminant and to the Rank of Multidimensional Matrices
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    Chapter 21 Commutative Algebra of Subspace and Hyperplane Arrangements
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    Chapter 22 Cohomological Degrees and Applications