Rationality Problems in Algebraic Geometry Levico Terme, Italy 2015

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments.  It offers a comprehensive introduction to this fascinating topic, and will certainly become an

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Arnaud Beauville · Brendan Hassett Alexander Kuznetsov Alessandro Verra

Rationality Problems in Algebraic Geometry Levico Terme, Italy 2015 Rita Pardini · Gian Pietro Pirola Editors

Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Michel Brion, Grenoble Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg

More information about this series at http://www.springer.com/series/304

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Arnaud Beauville • Brendan Hassett • Alexander Kuznetsov • Alessandro Verra

Rationality Problems in Algebraic Geometry Levico Terme, Italy 2015 Rita Pardini • Gian Pietro Pirola Editors

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Authors Arnaud Beauville Laboratoire J.-A. Dieudonné Université de Nice Nice cedex 2, France

Brendan Hassett ICERM, Brown University Brown University ICERM, Brown University Rhode Island Providence, USA

Alexander Kuznetsov Steklov Mathematical Institute of Russian Academy of Sciences Moscow, Russia

Alessandro Verra Dipartimento di Matematica UniversitJa Roma Tre Roma, Italy

Editors Rita Pardini Dipartimento di Matematica UniversitJa di Pisa Dipartimento di Matematica Pisa, Italy

Gian Pietro Pirola Dipartimento di matematica University of Pavia Pavia, Italy

ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-46208-0 DOI 10.1007/978-3-319-46209-7

ISSN 1617-9692 (electronic) ISBN 978-3-319-46209-7 (eBook)

Library of Congress Control Number: 2016958456 Mathematics Subject Classification (MSC2010): 14E08, 14F05, 14H10 © 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 Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

The Lüroth