A structure theorem along fibers of extreme points of the momentum polytope
Abstract
Let G be a complex reductive Lie group acting on a compact Kähler manifold X . 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 exists an associated open dense subset of X , that is invariant under the action of 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 this result. Additionaly, we establish a similar statement for real reductive subgroups of G and the restricted momentum map.
Fields of Study & Subjects
Geometry and complex manifolds
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Journal of Lie Theory
- Volume
- 36
- Issue
- 1
- Pages
- 51–76
- Publication date
- 17 June 2026
- Language
- EN