A structure theorem along fibers of extreme points of the momentum polytope

2025/05/11 by Heinzner, Peter, Zöller, Christian
#32M05 #Complex Variables (math.CV) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2505.07006

Abstract

Let G be a complex reductive Lie group acting on a compact Kähler manifold X and assume that the action of a maximal compact subgroup K of G is Hamiltonian. For each extreme point of the convex hull of the momentum map image, there is an associated open dense subset of X, which is invariant under a parabolic subgroup Q of G. We prove a Q-equivariant product decomposition for the Q-action on this subset and discuss some applications of the result. We show a similar statement for real reductive subgroups of G for the restricted momentum map.

Related

• Compact orbits of Parabolic subgroups
• Remarks on Semistable Points and Nonabelian Convexity of Gradient Maps
• Stability, analytic stability for real reductive Lie groups
• Properties of Gradient maps associated with Action of Real reductive Group
• Reductive group actions on Kähler manifolds