© 1998

Introduction to Liaison Theory and Deficiency Modules


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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Juan C. Migliore
    Pages 1-46
  3. Juan C. Migliore
    Pages 47-60
  4. Juan C. Migliore
    Pages 61-76
  5. Juan C. Migliore
    Pages 77-100
  6. Juan C. Migliore
    Pages 101-150
  7. Juan C. Migliore
    Pages 151-194
  8. Back Matter
    Pages 195-218

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.


Deficiency Modules Finite Invariant Liaison theory algebra calculus equation geometry theorem

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

Bibliographic information

  • Book Title Introduction to Liaison Theory and Deficiency Modules
  • Authors Juan C. Migliore
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Boston 1998
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4027-9
  • Softcover ISBN 978-1-4612-7286-1
  • eBook ISBN 978-1-4612-1794-7
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 2
  • Number of Pages XIII, 218
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
    Commutative Rings and Algebras
  • Buy this book on publisher's site


"Suitable for a graduate course in algebraic geometry...numerous discussions about the historical development, 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