This is a fundamental result of the theory of algebraic curves, having many applications however, none of the known proofs are entirely straightforward. The most substantial addition in the third edition is the proof of the Riemann– Roch theorem for curves, which was merely stated in previous editions. I could add a few more names, especially V.G. Other mathematicians who helped me in writing the book are mentioned in the preface to the first two editions. Reid, contributed some improvements with his careful reading of the text. In particular the translator of the second edition, M. In addition to this, both the first and the second edition were translated into English, and the publisher SpringerVerlag provided me with a number of remarks from Western mathematicians on the translation of the first edition. Popov, to whom I am grateful for a careful and thoughtful reading of the text. I was equally fortunate with the editor of the second edition, V.L. Moishezon worked as editor on the first edition, and the text reflects his advice and a number of his suggestions. Both of these are based on remarks and advice from readers of the earlier editions. The third edition differs from the previous two in some fairly minor corrections and a number of additions. Printed on acid-free paper Springer is part of Springer Science+Business Media (Preface The publisher makes no warranty, express or implied, with respect to the material contained herein. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. 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 use of general descriptive names, registered names, trademarks, service marks, etc. Violations are liable to prosecution under the respective Copyright Law. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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. MCCME, Moscow 2007, originally published in Russian in one volume © Springer-Verlag Berlin Heidelberg 1977, 1994, 2013 This work is subject to copyright. ISBN 978-5-0 ISBN 978-6-7 (eBook) DOI 10.1007/978-6-7 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013945284 Mathematics Subject Classification (2010): 14-01 Translation of the 3rd Russian edition entitled “Osnovy algebraicheskoj geometrii”. Translator Miles Reid Mathematics Institute University of Warwick Coventry, UK Shafarevich Algebra Section Steklov Mathematical Institute of the Russian Academy of Sciences Moscow, Russia Basic Algebraic Geometry 1 Varieties in Projective Space Third Edition
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