Introduction to Liaison Theory and Deficiency Modules
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 Univ
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Series Editors Hyman Bass Joseph Oesterle Alan Weinstein
Juan C. Migliore
Introduction to Liaison Theory and Deficiency Modules
Springer Science+Business Media, LLC
Juan C. Migliore Department of Mathematics University of Notre Dame Notre Dame, IN 46556
Library of Congress Cataloging-in-Publication Data Migliore, Juan C. (Juan Carlos), 1956Introduction to liaison theory and deficiency modules / Juan C. Migliore. p. cm. -- (progress in mathematics ; v. 165) Includes bibliographical references and index. ISBN 978-1-4612-7286-1 ISBN 978-1-4612-1794-7 (eBook) DOI 10.1007/978-1-4612-1794-7 1. Liaison theory (Mathematics) 2. Graded modules. 1. Title. II. Series: Progress in mathematics (Boston, Mass.); voI. 165. QA564.M49 1998 98-15680 516.3'5--dc21 CIP AMS Subject Classification: 14M06, 13C40, 14F05, 14M05, 14M07, 14MI0, 14M12, 13D02
Printed on acid-free paper © 1998 Springer Science+Business Media New York Origina\ly published by Birkha.user Boston in 1998 Softcover reprint ofthe hardcover 2nd edition 1998 Copyright is not claimed for works of U .S. Government employees. AlI rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. Authorization to photocopy items for internal or personal use of specific clients is granted by Springer Science+Business Media, LLC. provided that the appropriate fee is paid directly to Copyright Clearance Center (CCC), 222 Rosewood Drive, Danvers, MA 01923, USA (Telephone: (978) 750-8400), stating the ISBN, the title of the book, and the first and last page numbers of each article copied. The copyright owner's consent does not include copying for general distribution, promotion, new works, or resale. In these cases, specific wrltten permission must frrst be obtained from the publisher. ISBN 978-1-4612-7286-1 Typeset by the Author in Je..1EX
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To Michelle and Emily and Claire
Preface 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 resulted 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 liais
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