E-Book Overview
The theory of Frobenius splittings has made a significant impact in the study of the geometry of flag varieties and representation theory. This work, unique in book literature, systematically develops the theory and covers all its major developments.
Key features:
* Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research
* Studies in detail the geometry of Schubert varieties, their syzygies, equivariant embeddings of reductive groups, Hilbert Schemes, canonical splittings, good filtrations, among other topics
* Applies Frobenius splitting methods to algebraic geometry and various problems in representation theory
* Many examples, exercises, and open problems suggested throughout
* Comprehensive bibliography and index
This book will be an excellent resource for mathematicians and graduate students in algebraic geometry and representation theory of algebraic groups.
E-Book Content
Progress in Mathematics Volume 231
Series Editors Hyman Bass Joseph Oesterl´e Alan Weinstein
Michel Brion Shrawan Kumar
Frobenius Splitting Methods in Geometry and Representation Theory
Birkh¨auser Boston • Basel • Berlin
Michel Brion Universit´e Grenoble 1 – CNRS Institut Fourier 38402 St.-Martin d’H`eres Cedex France
Shrawan Kumar University of North Carolina Department of Mathematics Chapel Hill, NC 27599 U.S.A.
AMS Subject Classifications: 13A35, 13D02, 14C05, 14E15, 14F10, 14F17, 14L30, 14M05, 14M15, 14M17, 14M25, 16S37, 17B10, 17B20, 17B45, 20G05, 20G15 Library of Congress Cataloging-in-Publication Data Brion, Michel, 1958Frobenius splitting methods in geometry and representation theory / Michel Brion, Shrawan Kumar. p. cm. – (Progress in mathematics ; v. 231) Includes