Intersection Theory
From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has
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Editorial Board S. Feferman, Stanford N. H. Kuiper, Bures-sur-Yvette P. Lax, New York R. Remmert (Managing Editor), Munster W. Schmid, Cambridge, Mass. J-P. Serre, Paris 1. Tits, Paris
William Fulton
Intersection Theory
Springer-Verlag Berlin Heidelberg GmbH 1984
William Fulton Department of Mathematics Brown University Providence, RI 02912, USA
AMS-MOS (1980) Classification numbers: 14C17, 14-02, 14C10, 14C15, 14C25, 14C40, 14EI0, 14M12, 14M15, 14N10, 55N45 ISBN 978-3-662-02423-2 ISBN 978-3-662-02421-8 (eBook) DOI 10.1007/978-3-662-02421-8
Library of Congress Cataloging in Publication Data Fulton, William, 1939- Intersection theory. (Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 2) Bibliography: p. Includes index. I. Intersection theory. L Title. II. Series. QA564.F84 1984 512'.33 83-16762
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort," Munich. © Springer-Verlag Berlin Heidelberg 1984 Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1984 Softcover reprint of the hardcover 1st edition 1984
Preface
From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. Since its role in foundational crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive history of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to develop the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appendices. Some of the examples, and a few of the later sections, require more specialized knowledge. The text is designed so that one who understands the constructions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should facilitate use as a reference. Several theorems are new or stronger than those which have appeared before, and some proofs are significantly simpler. Among t
