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

Peter Heinzner; Christian Zöller

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arXiv · 2505.07006

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

Peter Heinzner·Christian Zöller

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Abstract

Let G be a complex reductive Lie group acting on a compact K\"ahler 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.

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Peter Heinzner, Christian Zöller. 2025-05-11. A structure theorem along fibers of extreme points of the momentum polytope. https://arxiv.org/abs/2505.07006

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