K3 Surfaces and Their Moduli
This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like
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Carel Faber Gavril Farkas Gerard van der Geer Editors
K3 Surfaces and Their Moduli
Progress in Mathematics Volume 315
Series Editors Hyman Bass, University of Michigan, Ann Arbor, USA Jiang-Hua Lu, The University of Hong Kong, Hong Kong SAR, China Joseph Oesterlé, Université Pierre et Marie Curie, Paris, France Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, USA
More information about this series at http://www.springer.com/series/4848
Carel Faber • Gavril Farkas • Gerard van der Geer Editors
K3 Surfaces and Their Moduli
Editors Carel Faber Mathematisch Instituut Universiteit Utrecht Utrecht, The Netherlands
Gavril Farkas Institut für Mathematik Humboldt Universität Berlin Berlin, Germany
Gerard van der Geer Korteweg-de Vries Instituut Universiteit van Amsterdam Amsterdam, The Netherlands
ISSN 0743-1643 ISSN 2296-505X (electronic) Progress in Mathematics ISBN 978-3-319-29958-7 ISBN 978-3-319-29959-4 (eBook) DOI 10.1007/978-3-319-29959-4 Library of Congress Control Number: 2016934933 Mathematics Subject Classification (2010): primary: 14J28, 14J15, 14J10, secondary: 14J32, 14J33, 14J50, 14N35 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, 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 any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser. The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com)
CONTENTS
Introduction The automorphism group of the Hilbert scheme of two points on a generic projective K3 surface Samuel Boissi`ere, Andrea Cattaneo, Marc Nieper-Wisskirchen, and Alessandra Sarti
vii 1
Orbital counting of curves on algebraic surfaces and sphere packings Igor Dolgachev
17
Moduli of polarized Enriques surfaces V. Gritsenko and K. Hulek
55
Extremal rays and automorphisms of holomorphic symplectic varieties Brendan Hassett and Yuri Tschinkel
73
An odd presentation for W (E6 ) Gert Heckman and Sander Rieken
97
On the motivic stable pairs invaria
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