An Invitation to Web Geometry
This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around
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Jorge Vitório Pereira Luc Pirio
An Invitation to Web Geometry
Instituto de Matemática Pura e Aplicada
IMPA Monographs Volume 2
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
Jorge Vitório Pereira Luc Pirio
An Invitation to Web Geometry
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Jorge Vitório Pereira Instituto de Matemática Pura e Aplicada Rio de Janeiro, Brazil
Luc Pirio Institut de Recherches Mathématiques de Rennes IRMAR, UMR 6625 du CNRS Université Rennes 1, Rennes France
IMPA Monographs ISBN 978-3-319-14561-7 ISBN 978-3-319-14562-4 (eBook) DOI 10.1007/978-3-319-14562-4 Library of Congress Control Number: 2015930015 Mathematics Subject Classification (2010): 53A60, 53A20, 14H 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)
Para Dayse e Jorge, os meus Pastores. J.V.P. Pour Min’ et Nin’ L.P.
Preface
The first purpose of this text was to serve as supporting material for a minicourse on web geometry delivered at the 27th Brazilian Mathematical Colloquium, which took place at IMPA in the last week of July 2009. Still, it contains much more than what can possibly be covered in five lectures of 1 h eac
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