Trends in Commutative Algebra

This book describes the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology, and combinatorics.

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

9780521168724, Cambridge University Press

Paperback, published 14 April 2011

266 pages
23.4 x 15.6 x 1.4 cm, 0.38 kg

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

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.

Preface
1. Commutative algebra in the cohomology of groups Dave Benson
2. Modules and cohomology over group algebras Srikanth Iyengar
3. An informal introduction to multiplier ideals Manuel Blickle and Robert Lazarsfeld
4. Lectures on the geometry of syzygies David Eisenbud, with a chapter by Jessica Sidman
5. Commutative algebra of n points in the plane Mark Haiman, with an appendix by Ezra Miller
6. Tight closure theory and characteristic p methods Melvin Hochster, with an appendix by Graham J. Leuschke
7. Monomial ideals, binomial ideals, polynomial ideals Bernard Teissier
8. Some facts about canonical subalgebra bases Ana Bravo.

Subject Areas: Algebra [PBF]