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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