scholarly journals Extension theorems for reductive group actions on compact Kaehler manifolds

1975 ◽  
Vol 81 (4) ◽  
pp. 729-733
Author(s):  
Andrew J. Sommese
Keyword(s):  
Group Actions ◽  
Reductive Group ◽  
Extension Theorems ◽  
Kaehler Manifolds

Deformations of reductive group actions

1989 ◽  
Vol 106 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Gerd Müller
Keyword(s):  
Lie Group ◽  
Tangent Space ◽  
Group Actions ◽  
Reductive Group ◽  
Analytic Space ◽  
Precise Formulation ◽  
The Given

Consider actions of a reductive complex Lie group G on an analytic space germ (X, 0). In a previous paper [16] we proved that such an action is determined uniquely (up to conjugation with an automorphism of (X, 0)) by the induced action of G on the tangent space of (X, 0). Here it will be shown that every deformation of such an action, parametrized holomorphically by a reduced analytic space germ, is trivial, i.e. can be obtained from the given action by conjugation with a family of automorphisms of (X, 0) depending holomorphically on the parameter. (For a more precise formulation in terms of actions on analytic ℂ-algebras, see Theorem 2 below. An analogue for actions on formal ℂ-algebras is given there too.)

scholarly journals Reductive group actions with one-dimensional quotient

1992 ◽  
Vol 76 (1) ◽  
pp. 1-97 ◽  
Author(s):  
Hanspeter Kraft ◽  
Gerald W. Schwarz
Keyword(s):  
Group Actions ◽  
Reductive Group ◽  
One Dimensional

scholarly journals NOTIONS OF PURITY AND THE COHOMOLOGY OF QUIVER MODULI

2012 ◽  
Vol 23 (09) ◽  
pp. 1250097 ◽  
Author(s):  
M. BRION ◽  
R. JOSHUA
Keyword(s):  
Finite Fields ◽  
Moduli Space ◽  
Group Actions ◽  
Reductive Group ◽  
Cohomology Groups ◽  
Dimension Vector ◽  
Principal Bundles ◽  
Fixed Dimension

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natural stratification of the space of representations of a quiver with a fixed dimension vector is equivariantly perfect and from it deduce that each of the l-adic cohomology groups of the quiver moduli space is strongly pure.

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