Classification of Irregular Varieties Minimal Models and Abelian Var
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1515
E. Ballico
F. Catanese C. Ciliberto (Eds.)
Classification of Irregular Varieties Minimal Models and Abelian Varieties Proceedings of a Conference held in Trento, Italy, 17-21 December, 1990
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Editors Edoardo Ballico Dipartimento di Matematica Universita di Trento 38050 Povo (Trento), Italy Fabrizio Catanese Dipartimento di Matematica Universita di Pisa Via F. Buonarroti 2, 56100 Pisa, Italy Ciro Ciliberto Dipartimento di Matematica Universita di Tor Vergata Via Fontanile di Carcaricola 00133 Roma, Italy
Mathematics Subject Classification (1991): 14H99, 14N05, 14NIO, 14J99
ISBN 3-540-55295-2 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-55295-2 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
CONTENTS
M. Andreatta, E. Ballico, J. Wisniewski - Projectivemanifolds containing large linear subspaces
1
F. Bardelli - Algebraic cohomology classes on some special threefolds
12
Ch. Birkenhake, H. Lange - Norm-endomorphisms of abelian subvarieties
21
C. Ciliberto, G. van der Geer - On the jacobian of a hyperplane section of a surface
33
C. Ciliberto, J. Harris, M. Teixidor i Bigas - On the endomorphisms of
and C has general moduli B. van Geemen - Projective models of Picard modular varieties
when p = 1 41 68
J. Kollar, Y. Miyaoka, S. Mori - Rational curves on Fano varieties
100
R. Salvati Manni - Modular forms of the fourth degree
106
A. Vistoli - Equivariant Grothendieck groups and equivariant Chow groups
112
Trento
134
examples
Open problems
140
List of participants
147
PREFACE The conference on "Classification of Irregular Varieties, Minimal Models and Abelian Varieties" was held in Villa Madruzzo, Cognola (Trento) from December 17 to 21,1990. The meeting has been sponsored and supported by C.LR.M. (Centro Intemazionale per la Ricerca Matematica, Trento), the Mathematical Department of the University of Trento and Centro Matematico Vito Volterra. This volume contains most of the works reported in the formal and informal lectures at the conference. The topics of the volume are: Abelian varieties and related varieties (papers by Bardelli, Birkenhake - Lange, Ciliberto Harris - Teixidor, Ciliberto - Van der Geer, Salva
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