Trends in Commutative Algebra

by Edited by Luchezar L. Avramov , Mark Green , Craig Huneke , Karen E. Smith , Bernd Sturmfels

• ISBN13: 9780521168724
• ISBN10: 0521168724
• Format: Paperback
• Copyright: 2011-04-14
• Publisher: Cambridge University Press

Summary

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 2005 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.

Table of Contents

Preface	p. ix
Commutative Algebra in the Cohomology of Groups	p. 1
Modules and Cohomology over Group Algebras	p. 51
An Informal Introduction to Multiplier Ideals	p. 87
Lectures on the Geometry of Syzygies	p. 115
Commutative Algebra of n Points in the Plane	p. 153
Tight Closure Theory and Characteristic p Methods	p. 181
Monomial Ideals, Binomial Ideals, Polynomial Ideals	p. 211
Some Facts About Canonical Subalgebra Bases	p. 247
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