**University Lecture Series**

Volume: 42;
2008;
190 pp;
Softcover

MSC: Primary 13; 14; 05;

Print ISBN: 978-0-8218-4434-2

Product Code: ULECT/42

List Price: $42.00

Individual Member Price: $33.60

**Electronic ISBN: 978-1-4704-2186-1
Product Code: ULECT/42.E**

List Price: $42.00

Individual Member Price: $33.60

#### Supplemental Materials

# Three Lectures on Commutative Algebra

Share this page *Edited by *
*Gemma Colomé-Nin; Teresa Cortadellas Benítez; Juan Elias; Santiago Zarzuela*

Holger Brenner, University of Sheffield, United Kingdom, Jürgen Herzog, Universität Duisburg-Essen, Germany, and Orlando Villamayor, Universidad Autónoma de Madrid, Spain

This book provides careful and detailed introductions to some of the
latest advances in three significant areas of rapid development in
commutative algebra and its applications. The book is based on courses at
the Winter School on Commutative Algebra and Applications held in
Barcelona: Tight closure and vector bundles, by H. Brenner; Combinatorics
and commutative algebra, by J. Herzog; and Constructive desingularization,
by O. Villamayor.

The exposition is aimed at graduate students who have some experience with
basic commutative algebra or algebraic geometry but may also serve as an
introduction to these modern approaches for mathematicians already
familiar with commutative algebra.

This book is published in cooperation with Real Sociedad Matemática Española (RSME)

#### Table of Contents

# Table of Contents

## Three Lectures on Commutative Algebra

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Tight Closure and Vector Bundles 110 free
- Introduction 514
- Chapter 1. Tight closure 716
- Chapter 2. Forcing algebras and affine-linear bundles 1524
- Chapter 3. Principal fiber bundles (torsors) and their projective realization 2332
- Chapter 4. Ample vector bundles 3140
- Chapter 5. Semistable bundles and the Harder-Narasimhan filtration 3746
- Chapter 6. Numerical inclusion criteria for tight closure 4352
- Chapter 7. Numerical criteria for affineness of torsors 4958
- Chapter 8. Tight closure and plus closure in graded dimension two 5362
- Chapter 9. Hilbert-Kunz theory 5766
- Chapter 10. Deformations of tight closure and the localization problem 6372
- Bibliography 6978

- Combinatorics and Commutative Algebra 7382
- Notes on Constructive Desingularization 123132
- Back Cover Back Cover1202

#### Readership

Graduate students and research mathematicians interested in commutative algebra and algebraic geometry.