Trends in Commutative Algebra

Mathematical Sciences Research Institute

doi:10.1017/CBO9780511756382

In 2002, an introductory workshop was held at the Mathematical Sciences Research Institute in Berkeley to survey some of the many directions of the commutative algebra field. Six principal speakers each gave three lectures, accompanied by a help session, describing the interaction of commutative algebra with other areas of mathematics for a broad audience of graduate students and researchers. This book is based on those lectures, together with papers from contributing researchers. David Benson and Srikanth Iyengar present an introduction to the uses and concepts of commutative algebra in the cohomology of groups. Mark Haiman considers the commutative algebra of n points in the plane. Ezra Miller presents an introduction to the Hilbert scheme of points to complement Professor Haiman's paper. Further contributors include David Eisenbud and Jessica Sidman; Melvin Hochster; Graham Leuschke; Rob Lazarsfeld and Manuel Blickle; Bernard Teissier; and Ana Bravo.

Review of the hardback:‘… invaluable reading for graduate students and researchers interested in commutative algebra and its various uses.‘

Source: L'Enseignement Mathématique

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Trends in Commutative Algebra

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-x

Commutative Algebra in the Cohomology of Groups
pp 1-50

Modules and Cohomology over Group Algebras: One Commutative Algebraist’s Perspective
pp 51-86

An Informal Introduction to Multiplier Ideals
pp 87-114

Lectures on the Geometry of Syzygies
pp 115-152

Commutative Algebra of n Points in the Plane
pp 153-180

Tight Closure Theory and Characteristic p Methods
pp 181-210

Monomial Ideals, Binomial Ideals, Polynomial Ideals
pp 211-246

Some Facts About Canonical Subalgebra Bases
pp 247-254

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Trends in Commutative Algebra

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