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Introduction to Liaison Theory and Deficiency Modules

  • Book
  • © 1998

Overview

Authors:
  1. Juan C. Migliore

    1. Department of Mathematics, University of Notre Dame, Notre Dame, USA

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Part of the book series: Progress in Mathematics (PM, volume 165)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Background

    • Juan C. Migliore
    Pages 1-46

  3. Submodules of the Deficiency Module

    • Juan C. Migliore
    Pages 47-60

  4. Buchsbaum Curves and Liaison Addition

    • Juan C. Migliore
    Pages 61-76

  5. Gorenstein Subschemes of Projective Space

    • Juan C. Migliore
    Pages 77-100

  6. Liaison Theory in Arbitrary Codimension

    • Juan C. Migliore
    Pages 101-150

  7. Liaison Theory in Codimension Two

    • Juan C. Migliore
    Pages 151-194

  8. Back Matter

    Pages 195-218
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Keywords

About this book

In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks. I was asked to write a monograph based on my talks, and the result was published by the Global Analysis Research Center of that University in 1994. The monograph treated deficiency modules and liaison theory for complete intersections. Over the next several years I continually thought of improvements and additions that I would like to make to the manuscript, and at the same time my research led me in directions that gave me a fresh perspective on much of the material, especially in the direction of liaison theory. This re­ sulted in a dramatic change in the focus of this manuscript, from complete intersections to Gorenstein ideals, and a substantial amount of additions and revisions. It is my hope that this book now serves not only as an introduction to a beautiful subject, but also gives the reader a glimpse at very recent developments and an idea of the direction in which liaison theory is going, at least from my perspective. One theme which I have tried to stress is the tremendous amount of geometry which lies at the heart of the subject, and the beautiful interplay between algebra and geometry. Whenever possible I have given remarks and examples to illustrate this interplay, and I have tried to phrase the results in as geometric a way as possible.

Reviews

"Suitable for a graduate course in algebraic geometry...numerous discussions about the historical development, and...an ample and useful list of references to important original sources... Relations between linked schemes...are explained in great detail, with complete proofs and numerous examples. ...The book ends with a section which gives a flavour of some of the ways in which liaison theory has been applied in the literature. Many more applications and examples are spread throughout the text. They contribute to a lively and inspiring style. This book is a worthwhile addition to every algebraic geometer's library."

--Mathematical Reviews

"A highly specialized monograph that provides a very good introduction to contemporary research in the fields of liaison theory and deficiency modules... The author pays great attention to motivation and the geometric aspects of the theory. There are many examples through which the reader is introduced into the theory, thereby stimulating research in the field... Useful both for specialists and for postgraduate students."

--EMS Newsletter

Authors and Affiliations

  • Department of Mathematics, University of Notre Dame, Notre Dame, USA

    Juan C. Migliore

Bibliographic Information

  • Book Title: Introduction to Liaison Theory and Deficiency Modules

  • Authors: Juan C. Migliore

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1794-7

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1998

  • Hardcover ISBN: 978-0-8176-4027-9Published: 25 August 1998

  • Softcover ISBN: 978-1-4612-7286-1Published: 21 October 2012

  • eBook ISBN: 978-1-4612-1794-7Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 2

  • Number of Pages: XIII, 218

  • Topics: Algebraic Geometry, Commutative Rings and Algebras, Algebra

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