Period Mappings with Applications to Symplectic Complex Spaces
Extending Griffiths’ classical theory of period mappings for compact Kähler manifolds, this book develops and applies a theory of period mappings of “Hodge-de Rham type” for families of open complex manifolds. The text consists of three parts. The first p
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Tim Kirschner
Period Mappings with Applications to Symplectic Complex Spaces
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and NY Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Tim Kirschner
Period Mappings with Applications to Symplectic Complex Spaces
123
Tim Kirschner Mathematisches Institut UniversitRat Bayreuth Bayreuth, Germany
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-17520-1 DOI 10.1007/978-3-319-17521-8
ISSN 1617-9692
(electronic)
ISBN 978-3-319-17521-8
(eBook)
Library of Congress Control Number: 2015948870 Mathematics Subject Classification (2010): 14F05 (also 18F20, 32C35), 32C20 (also 14D05, 14D07), 32S35, 14J32 (or 32Q25), 18G40 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
To my parents
Preface
Through this book, I intend to deliver to readers three chapters of state-of-the-art mathematics positioned at the crossroad of algebraic geometry—more precisely, the homological algebra of sheaves of modules on ringed spaces—and the theory of complex analytic spaces. From my perspective as the author, the focal point of the text is Chap. 1. The first chapter explores the territory surrounding Nicholas Katz’s and Tadao Oda’s conception of a Gauß-Manin connection defined on the relative algebraic de Rham cohomology sheaf. Here, I attempt to employ Katz’s and Oda’s idea in the realm of complex analytic spaces—to my knowledge for the first time in the lite
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