A. Bialynicki-Birula>, W. M. McGovern>, J. Carrell>

Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action

Softcover reprint of the original 1st edition 2002. Sprache: Englisch.

kartoniert , 252 Seiten

ISBN 3642077455

EAN 9783642077456

Veröffentlicht Oktober 2011

Verlag/Hersteller Springer Berlin Heidelberg

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Beschreibung

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 algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.