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Trends in Commutative Algebra

Trends in Commutative Algebra

Part of Mathematical Sciences Research Institute Publications

Dave Benson, Srikanth Iyengar, Manuel Blickle, Robert Lazarsfeld, David Eisenbud, Jessica Sidman, Mark Haiman, Ezra Miller, Melvin Hochster, Graham J. Leuschke, Bernard Teissier, Ana Bravo
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  • Date Published: February 2005
  • availability: Available
  • format: Hardback
  • isbn: 9780521831956

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  • 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.

    • Top-notch contributors
    • Broad scope of lectures
    • Many interesting open questions and fresh directions presented in the book
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    Reviews & endorsements

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

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    Product details

    • Date Published: February 2005
    • format: Hardback
    • isbn: 9780521831956
    • length: 266 pages
    • dimensions: 234 x 156 x 16 mm
    • weight: 0.51kg
    • availability: Available
  • Table of Contents

    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.

  • Editors

    Luchezar L. Avramov, University of Nebraska, Lincoln

    Mark Green, University of California, Los Angeles

    Craig Huneke, University of Kansas

    Karen E. Smith, University of Michigan, Ann Arbor

    Bernd Sturmfels, University of California, Berkeley

    Contributors

    Dave Benson, Srikanth Iyengar, Manuel Blickle, Robert Lazarsfeld, David Eisenbud, Jessica Sidman, Mark Haiman, Ezra Miller, Melvin Hochster, Graham J. Leuschke, Bernard Teissier, Ana Bravo

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