Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action
This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebr
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Invariant Theory and Algebraic Transformationgroups Subseries Editors: R. V. Gamkrelidze V.L. Popov
Springer-Verlag Berlin Heidelberg GmbH
A. Bialynicki-Birula
J. B. Carrell W. M. McGovern
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action
Springer
Andrzej Bialynicki-Birula Warsaw University Department of Mathematics and Computer Science Banacha2 02-097 Warsaw Poland e-mail: [email protected] James B. Carrell The University of British Columbia Department of Mathematics 1984 Mathematics Road Vancouver V 6T 1Z2 Canada e-mail: [email protected] William M. McGovern University of Washington Department of Mathematics P.O. Box 354350 Seattle, W A 98195 USA e-mail: [email protected]
Founding Editor of the Encyclopaedia of Mathematical Sciences: R.V. Gamkrelidze
Mathematics Subject Classification (2000): 14L30, 14LIO, 14L15, 14L17, 14L24, 14F25, 14F43, 14022, 13A50, 14M17, 14M25, 14M20, 22E46, 22E60, 22E20, 22E25, 20G05, 20G15, 22E45, 22E46
ISSN 0938-0396 ISBN 978-3-642-07745-6
ISBN 978-3-662-05071-2 (eBook)
DOI 10.1007/978-3-662-05071-2
This work is subject to copyright. AU rights reserved, whether the whole or part of the material is concerned, specifically of translation, reprinting, reuse of iIIustrations, 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-Verlag. Violations are Iiable for prosecution under the German Copyright Law. http://www.springer.de @Springer-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg New York in 2002 Softcover reprint of the hardcover lst edition 2002 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 and Production: LE-1J3X Jelonek, Schmidt & Vockler GbR, Leipzig Cover Design: E. Kirchner, Heidelberg, Germany Printed on acid-free paper SPIN: 10986752 46/3111 54 321
Contents I. Quotients by Actions of Groups Andrzej Bialynicki-Birula 1 ll. Torus Actions and Cohomology
James B. Carrell 83 llI. The Adjoint Representation and the Adjoint Action
William M. McGovern 159 SUbject Index
239
I. Quotients by Actions of Groups Andrzej Bialynicki-Birula
Contents Chapter 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Chapter 2
Terminology and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Spaces, Schemes, Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preequivalence Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Groupoids . .
