Graded Syzygies

  • Irena¬†Peeva

Part of the Algebra and Applications book series (AA, volume 14)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Irena Peeva
    Pages 1-158
  3. Irena Peeva
    Pages 159-204
  4. Irena Peeva
    Pages 205-254
  5. Irena Peeva
    Pages 255-287
  6. Back Matter
    Pages 289-302

About this book

Introduction

The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts.

A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration.

The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions  over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.

Keywords

Free resolutions Graded commutative rings Hilbert functions

Authors and affiliations

  • Irena¬†Peeva
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-177-6
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-176-9
  • Online ISBN 978-0-85729-177-6
  • About this book