Degenerations of Hodge Structures
Usually, families come with singular fibres and it is very interesting to investigate what happens near such a fibre. In this monograph we mostly consider 1-parameter degenerations, where the base is a punctured disk and the family is smooth over the punc
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A Series of Modern Surveys in Mathematics
Editorial Board S. Feferman, Stanford M. Gromov, Bures-sur-Yvette J. Jost, Leipzig J. Koll´ar, Princeton G. Laumon, Orsay H. W. Lenstra, Jr., Leiden P.-L. Lions, Paris M. Rapoport, Köln J. Tits, Paris D. B. Zagier, Bonn G. Ziegler, Berlin Managing Editor R. Remmert, Münster
Volume 52
Chris A. M. Peters · Joseph H. M. Steenbrink
Mixed Hodge Structures
123
Prof. Dr. Chris A. M. Peters Université de Grenoble I Institut Fourier UFR de Mathématiques 100 rue de Maths 38402 Saint-Martin d’Hères France [email protected]
Prof. Dr. Joseph H. M. Steenbrink Radboud University Nijmegen Department of Mathematics Toernooiveld 1 6525 ED Nijmegen Netherlands [email protected]
ISBN 978-3-540-77015-2
e-ISBN 978-3-540-77017-6
DOI 10.1007/978-3-540-77017-6 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ISSN 0071-1136 Library of Congress Control Number: 2007942592 Mathematics Subject Classification (2000): 14C30, 14D07, 32C38, 32G20, 32S35, 58A14 © 2008 Springer-Verlag Berlin Heidelberg 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 microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, 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. Typesetting: by the author using a Springer TEX macro package Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper 9 87654321 springer.com
Preface
The text of this book has its origins more than twenty-five years ago. In the seminar of the Dutch Singularity Theory project in 1982 and 1983, the second-named author gave a series of lectures on Mixed Hodge Structures and Singularities, accompanied by a set of hand-written notes. The publication of these notes was prevented by a revolution in the subject due to Morihiko Saito: the introduction of the theory of Mixed Hodge Modules around 1985. Understanding this theory was at the same time of great importance and very hard, due to the fact that it unifies many different theories which are quite complicated themselves: algebraic D-modules and perverse sheaves. The present book intends to provide a comprehensive text about Mixed Hodge Theory with a view towards Mixed Hodge Modules. The approach to Hodge theory for singular spaces is due to Navarro and his collaborators, whose
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