Joins and Intersections
Dedicated to the memory of Wolfgang Classical Intersection Theory (see for example Wei! [Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a non singular variety) intersect with the expected dimension. In 1
- PDF / 27,933,773 Bytes
- 307 Pages / 439.37 x 666.142 pts Page_size
- 67 Downloads / 249 Views
Springer-Verlag Berlin Heidelberg GmbH
H. Flenner • L. O'Carroll • W. Vogel
Joins
and
Intersections
,
Springer
Hubert Flenner Fakultiit rur Mathematik Ruhr- Universitiit Bochum Geb.NA 2/72 D-44780 Bochum Germany
Liam O'Carroll
Department of Mathematics and Statistics University of Edinburgh King's Building Edinburgh, EH9 3JZ United Kingdom
Wolfgang Vogel t
Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Flenner, Hubert:
Joins and intersections / H. Flenner; L. O'Carroll; W. Vogel. Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris ; Singapore ; Tokyo : Springer, 1999 (Springer Monographs in mathematics)
Mathematics Subject Classification (1991): 14C17, 13HI5, 14-02, 14A05
ISBN 978-3-642-08562-8 ISBN 978-3-662-03817-8 (eBook) DOI 10.1007/978-3-662-03817-8 Sof'tcover reprint of the hardcover 1st edition 1999 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. C> Springer-Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg New York in 1999. The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Cover design: Erich Kirchner, Heidelberg Typeset by the authors using a Springer ~ macro package SPIN 10705513
44/3143LK-S4321 0 - Printed on acid-free paper
Table of Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 5
1.
The Classical Bezout Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Degrees of Projective Schemes ........................... 1.2 Multiplicities of Local Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1.3 Joins.................................................. 1.4 The Classical Bezout Theorem .......................... 1.5 Generic Bertini Theorems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
7 7 12 24 32 36
2.
The 2.1 2.2 2.3 2.4 2.5
Intersection Algorithm and Applications. . . . . . . . . . . .. The Intersection Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Application I: The Refined Bezout Theorem ............... Segre Classes, v-Cycles and Positivity. . . . . . . . . . .
