Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint ActionSpringer Science & Business Media, 24.04.2002 - 242 Seiten 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. |
Inhalt
II | 4 |
III | 5 |
IV | 7 |
V | 8 |
VI | 10 |
VII | 12 |
X | 13 |
XI | 14 |
LXIV | 133 |
LXVI | 139 |
LXVII | 144 |
LXVIII | 147 |
LXIX | 151 |
LXX | 154 |
159 | |
LXXII | 162 |
XII | 16 |
XIV | 17 |
XV | 19 |
XVI | 20 |
XVII | 21 |
XIX | 22 |
XX | 23 |
XXI | 25 |
XXII | 27 |
XXIII | 28 |
XXIV | 29 |
XXV | 30 |
XXVI | 31 |
XXVIII | 37 |
XXIX | 38 |
XXX | 39 |
XXXI | 42 |
XXXII | 47 |
XXXIII | 51 |
XXXIV | 53 |
XXXV | 54 |
XXXVI | 56 |
XXXVII | 57 |
XXXVIII | 59 |
XXXIX | 60 |
XL | 64 |
XLI | 65 |
XLII | 69 |
XLIII | 76 |
XLIV | 77 |
83 | |
XLVI | 85 |
XLVII | 87 |
XLIX | 89 |
L | 93 |
LI | 95 |
LII | 96 |
LIV | 97 |
LV | 99 |
LVI | 102 |
LVII | 108 |
LVIII | 109 |
LIX | 112 |
LX | 117 |
LXI | 119 |
LXII | 126 |
LXIII | 129 |
LXXIV | 163 |
LXXVI | 165 |
LXXVII | 166 |
LXXVIII | 167 |
LXXX | 169 |
LXXXI | 170 |
LXXXII | 171 |
LXXXIII | 172 |
LXXXIV | 174 |
LXXXV | 176 |
LXXXVI | 178 |
LXXXVII | 180 |
LXXXVIII | 182 |
LXXXIX | 184 |
XC | 185 |
XCI | 187 |
XCII | 188 |
XCIII | 189 |
XCIV | 190 |
XCV | 192 |
XCVII | 194 |
XCVIII | 195 |
XCIX | 196 |
C | 197 |
CI | 198 |
CII | 200 |
CIII | 208 |
CVI | 210 |
CVII | 212 |
CVIII | 216 |
CX | 217 |
CXII | 219 |
CXIII | 220 |
CXIV | 221 |
CXV | 222 |
CXVI | 223 |
CXVII | 224 |
CXVIII | 225 |
CXIX | 226 |
CXX | 228 |
CXXII | 229 |
CXXIII | 230 |
CXXIV | 231 |
CXXV | 232 |
239 | |
Andere Ausgaben - Alle anzeigen
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint ... A. Bialynicki-Birula,J. Carrell,W.M. McGovern Eingeschränkte Leseprobe - 2013 |
Algebraic Quotients. Torus Actions and Cohomology. the Adjoint ... A Bialynicki-Birula,J Carrell,W M McGovern Keine Leseprobe verfügbar - 2002 |
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint ... A. Bialynicki-Birula,J. Carrell,W.M. McGovern Keine Leseprobe verfügbar - 2011 |
Häufige Begriffe und Wortgruppen
action of G affine algebra g algebraic group algebraic space algebraic variety algebraically closed BB,Św Białynicki-Birula Borel subalgebra canonical Cartan subalgebra categorical quotient cells CG(x closure cohomology complex components compute conjugacy class contains corresponding decomposition defined denote diagram dimension equivalence relation equivariant example exists finite fixed point set formula G-invariant G-orbit geometric quotient GL(V Gm-action group G groupoid Hence homology induced irreducible isomorphism Lemma Levi subalgebra linear Math maximal torus moduli space Moreover morphism nilpotent element nilpotent orbits nilradical normal obtained open subset pair parabolic subalgebra parametrized partition Poincaré polynomial projective variety proof quotient space rationally smooth reductive group representation result ring S-scheme S-spaces Schubert varieties semi-stable semisimple Lie algebra simple roots Springer standard triple subgroup of G subspace subvariety surjective T-variety Theorem theory toric variety torus actions unipotent unique vector field W₁ Weyl group zero