An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
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Editorial Board W. Beiglböck, Institute of Applied Mathematics, University of Heidelberg, Germany J.-P. Eckmann, Department of Theoretical Physics, University of Geneva, Switzerland H. Grosse, Institute of Theoretical Physics, University of Vienna, Austria M. Loss, School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA S. Smirnov, Mathematics Section, University of Geneva, Switzerland L. Takhtajan, Department of Mathematics, Stony Brook University, NY, USA J. Yngvason, Institute of Theoretical Physics, University of Vienna, Austria
Martin Schlichenmaier
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces Second Edition With 21 Figures
Prof. Dr. Martin Schlichenmaier University of Luxembourg Institute of Mathematics 162A, avenue de la Faiencerie 1511 Luxembourg City Grand-Duchy of Luxembourg
Martin Schlichenmaier, An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, Theoretical and Mathematical Physics (Springer, Berlin Heidelberg 2007) DOI 10.1007/b11501497
Library of Congress Control Number: 2007926181 ISSN 0172-5998 ISBN 978-3-540-71174-2 Springer Berlin Heidelberg New York 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 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 authors and Integra Software Services Pvt. Ltd., Puducherry, India Cover design: eStudio Calamar, Girona/Spain Printed on acid-free paper
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Preface to the Second Edition
During the second advent of string theory the first edition of this Springer Lecture Notes volume appeared in 1990. There was an increasing demand for physicists to learn more about the modern aspects of geometry. In particular, for a further development of the physical theory the notions mentioned in the title turned out to be of fundamental importance. The first edition was based on lecture courses I gave at the Institute of Theoretical Physics, University of Karlsruhe, Germany. During this time the institute was headed by Prof. Julius Wess. Indeed, it was him who convinced me to write them up. Instead of repeating everything let me refer to the Introduction to the 1st Edition which can be found essentially
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