Algebraic Geometry and Analytic Geometry Proceedings of a Conference Held in Tokyo, Japan August 13-17, 1990

Home , Algebraic geometry, Analytic geometry

ICM-90 Satellite Conference Proceedings

A. Fujiki . K. Kato . T. Katsura Y. Kawamata . Y. Miyaoka (Eds.)

Algebraic Geometry and Analytic Geometry Proceedings of a Conference held in Tokyo, Japan August 13-17, 1990

Springer-Verlag Tokyo Berlin Heidelberg New York London Paris Hong Kong Barcelona Editors Akira Fujiki College of General Education, Kyoto University Yoshida-nihonmatsu, Sakyo-ku, Kyoto, 606 Japan

Kazuya Kato and Yujiro Kawamata Department of Mathematics, University of Tokyo Hongo, Bunkyo-ku, Tokyo, 113 Japan

Toshiyuki Katsura Department of Mathematics, Ochanomizu University Otsuka, Bunkyo-ku, Tokyo, 112 Japan

Yoichi Miyaoka Department of Mathematics, Rikkyo University Nishi-ikebukuro, Toshima-ku, Tokyo, 171 Japan

Mathematics Subject Classification (1980): 14-06, 14F99, 14J28, 14K99,14L99

ISBN-13:978-4-431-70086-9 e-ISBN-13:978-4-431-68172-4 DOl: 10.1007/978-4-431-68172-4

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 microfilms or in other ways, and storage in data banks. The use of 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. Preface

The International Conference "Algebraic Geometry and Analytic Geometry, Tokyo 1990" was held at Tokyo Metropolitan University and the Tokyo Training Center of Daihyaku Mutual Life Insurance Co., from August 13 through August 17, 1990, under the co-sponsorship of the Mathematical Society of Japan. It was one of the satellite conferences of ICM90, Kyoto, and approximately 300 participants, including more than 100 from overseas, attended the conference. The academic program was divided into two parts, the morning sessions and the afternoon sessions. The morning sessions were held at Tokyo Metropolitan University, and two one-hour plenary lectures were delivered every day. The afternoon sessions at the Tokyo Training Center, intended for a more specialized audience, consisted of four separate subsessions: Arithemetic Geometry, Algebraic Geometry, Analytic Geometry I and Analytic Geometry II. This book contains papers which grew out of the talks at the conference. The committee in charge of the organization and program consisted of A. Fujiki, K. Kato, T. Katsura, Y. Kawamata, Y. Miyaoka, S. Mori, K. Saito, N. Sasakura, T. Suwa and K. Watanabe. We would like to take this opportunity to thank the many mathematicians and students who cooperated to make the conference possible, especially Professors T. Fukui, S. Ishii, Y. Kitaoka, M. Miyanishi, Y. Namikawa, T. Oda, F. Sakai and T. Shioda for their valuable advice and assistance in organizing this conference. Financial support was mainly provided by personal contributions from Professors M. Nagata, T. Shioda and S. Iitaka as well as grants and fellowships from the following in• stitutions:

The Inamori Foundation, Inoue Foundation for Science, Japan Association for Mathematical Sciences, The Nikko Securities Co., Ltd. Tokyo Metropolitan Univ ..

We would like to thank Tokyo Metropolitan University for making available the lecture hall for the morning sessions. Last, but not least, we would like to express our hearty gratitude to Daihyaku Mutual Life Insurance Co. for generously providing facilities and accommodations.

The editors

Tokyo, April 1991 CONTENTS

V. BALAJI and C. S. SESHADRI, Poincare polynomials of some moduli varieties • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1

F. A. BOGOMOLOV, On two conjectures in birational algebraic geometry·· 26

HeUme ESNAULT and Eckart VIEHWEG, Ample sheaves on moduli schemes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 53

Shihoko ISHII, Simultaneous canonical models of deformations of isolated singularities • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 81

Janos KOLLAR, Cone theorems and cyclic covers •••••••••••••••••••••• 101

L:8 Dung Trang, Depth and perversity •••••••••••••••••••••••••••••••• 111

Noboru NAKAYAMA, Elliptic fibrations over surfaces I ••••••••••••••••• 126

Viacheslav V. NIKULIN, Weillinear systems on singular I<3 surfaces •••••• 138

Takashi SAITO, The Euler numbers of f-adic sheaves of rank 1 in positive characteristic •••••••••••••••••••••••••••••••••••••••••••••••••••••• 165

Vadim V. SCHECHTMAN and Alexander N. VARCHENKO, Quantum groups and homology of local systems ••••••••••••••••••••••••••••••••• 182

Carlos T. SIMPSON, A lower bound for the size of monodromy of systems of ordinary differential equations •••••••••••••••••••••••••••••••••••••• 198

Yuri G. ZARHIN, Abelian varieties of I<3 type and f-adic representations •• 231

List of talks •••••••••••••••••••••••••••••••••••••••••••••••••••••• 256 List of Participants ••••••••••••••••••••••••••••••••••••••••••••••••• 258