Hyperbolicity of Projective Hypersurfaces
This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic ge
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Simone Diverio Erwan Rousseau
Hyperbolicity of Projective Hypersurfaces Instituto de Matemática Pura e Aplicada
IMPA Monographs Volume 5
This series, jointly established by IMPA and Springer, publishes advanced monographs giving authoritative accounts of current research in any field of mathematics, with emphasis on those fields that are closer to the areas currently supported at IMPA. The series gives well-written presentations of the “state-of-the-art” in fields of mathematical research and pointers to future directions of research.
Series Editors Emanuel Carneiro, Instituto de Matemática Pura e Aplicada Severino Collier, Universidade Federal do Rio de Janeiro Claudio Landim, Instituto de Matemática Pura e Aplicada Paulo Sad, Instituto de Matemática Pura e Aplicada
More information about this series at http://www.springer.com/series/13501
Simone Diverio • Erwan Rousseau
Hyperbolicity of Projective Hypersurfaces
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Simone Diverio CNRS, Institut de Mathématiques de Jussieu - Paris Rive Gauche Sorbonne Universités Univ Paris Diderot Sorbonne Paris Cité Paris, France
Erwan Rousseau Aix Marseille Université CNRS, Centrale Marseille Marseille, France
IMPA Monographs ISBN 978-3-319-32314-5 ISBN 978-3-319-32315-2 (eBook) DOI 10.1007/978-3-319-32315-2 Library of Congress Control Number: 2016939013 © 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 Switzerland
Preface to the first edition
These are lecture notes of a course held at IMPA, Rio de Janeiro, in September 2010: the purpose was to present recent results on Kobayashi hyperbolicity in complex geometry. This area of research is very active, in particular because of the fascinating relations between analytic and arithmetic geometry. After Lang and Vojta, we have precise conjectures between analytic and arithmetic hyper
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