Complex Algebraic Varieties Proceedings of a Conference held in Bayr

The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to tal

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1507

K. Hulek T. Petemell F.-D. Schreyer (Eds.)

M. Schneider

Complex Algebraic Varieties Proceedings of a Conference held in Bayreuth, Germany, April 2-6, 1990

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest

Editors Klaus Hulek Fachbereich Mathematik Universitat Hannover Welfengarten I W-3000 Hannover, Germany Thomas Peternell Michael Schneider Frank-Olaf Schreyer Mathematisches Institut Universitat Bayreuth Postfach 101251 W-8580 Bayreuth, Germany

Mathematics Subject Classification (l991): 14DXX, 14EXX, 14FXX, 14JXX, 14KXX, 32LXX, 53CXX

ISBN 3-540-55235-9 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-55235-9 Springer-Verlag New York Berlin Heidelberg 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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. © Springer-Verlag Berlin Heidelberg 1992 Printed in Germany Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr, 46/3140-543210 - Printed on acid-free paper

Preface

This volume contains the proceedings of the conference" Complex Algebraic Varieties" held in Bayreuth from April 2-6, 1990. The main topic of this meeting was the classification of algebraic varieties including related topics. such as vector bundles. Most of the contributions are closely related to talks given by one of the authors at the conference. All the papers are original research articles. The conference was organized as part of the activities of the DFG research programme "Komplexe Mannigfaltigkeiten". We should like to thank the DFG for the financial support which made this conference possible. We are grateful to the University of Bayreuth for their hospitality. This conference profited greatly from the political changes of the last two years. It was one of the first conferences in Algebraic Geometry at which mathematicians from Eastern countries could participate without restrictions. exchange of ideas during the meeting. January 1992

K. Hulek Th. Peternell M. Schneider F.-O. Schreyer

This contributed greatly to a fruitful

Table of Contents

A. Beauville: Annulation du HI pour les fibres en droites plats

1

M. Beltrametti, A. J. Sommese, J. A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory

16

G. Bohnhorst, H. The stability of certain vector bundles on r;

39

F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of

11",

O. Debarre: Vers une stratification de l'espace des modules des varietes abeliennes principaiement polarisees

51

71

J. P.