Moduli of Abelian Varieties
Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from th
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Series Editors H. Bass
1. Oesterle A. Weinstein
Moduli of Abelian Varieties CareI Faber Gerard van der Geer Frans Oort Editors
Springer Basel AG
Editors: Carei Faber Institutionen for Matematik Kungliga Tekniska H6gskolan (KTH) 10044 Stockholm Sweden
Gerard van der Geer Korteweg de Vries Instituut Universiteit van Amsterdam Plantage Muidergracht 24 10 18 TV Amsterdam The Netherlands
Frans Oort Mathematisch Instituut Universiteit Utrecht Budapestlaan 6 3508 TA Utrecht The Netherlands 2000 Mathematics Subject Classification 14J60, 14D20, 11 G 15
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Moduli of Abelian varieties / Carei Faber ... ed. - Basel ; Boston; Berlin: 2001 (Progress in mathematics ; VoI. 195) ISBN 978-3-0348-9509-5 ISBN 978-3-0348-8303-0 (eBook) DOI 10.1007/978-3-0348-8303-0
Birkhăuser,
This work is subject to copyright. AH rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind ofuse whatsoever, permission from the copyright owner must be obtained. © 2001 Springer Basel AG Originally published by Birkhăuser Verlag in 2001 Softcover reprint of the hardcover 1st edition 2001
Printed on acid-free paper produced of chlorine-free pulp. TCF 00 ISBN 978-3-0348-9509-5 987654321
CONTENTS
Participants
vii
Contributors
IX
Introduction
xi
On extra components in the functorial compactification of A g V. Alexeev On Mumford's uniformization and Neron models of Jacobians of semistable curves over complete rings F. Andreatta
1
11
Torelli theorem via Fourier-Mukai transform A. Beilinson and A. Polishchuk
127
On the Andre-Oort conjecture for Hilbert modular surfaces B. Edixhoven
133
Toroidal resolutions for some matrix singularities G. Faltings
157
Formal Brauer groups and moduli of abelian surfaces G. van der Geer and T. Katsura
185
Isogeny classes of abelian varieties with no principal polarizations E. Howe
203
Igusa's modular form and the classification of Siegel modular threefolds K. Hulek
217
Mirror symmetry and quantization of abelian varieties Yu.I. Manin
231
Group schemes with additional structures and Weyl group cosets B. Moonen
255
Moduli space of elliptic curves with Heisenberg level structure I. Nakamura and T. Terasoma
299
Singularities of the height strata in the moduli of K3 surfaces A.Ogus
325
v
A stratification of a moduli space of abelian varieties
345
F. Dort Newton polygon strata in the moduli space of abelian varieties
417
The dimension of Oort strata of Shimura varieties of PEL-type T. Wedhorn
441
Hyperelliptic Jacobians and modular representations Yu. G. Zarhin
473
Windows for displays of p-divisible groups Th. Zink
491
F. Dort
vi
PARTICIPANTS
The following is the list of participants of the conference Moduli of Abelian Varieties, Texel '99,
