HKKN-stratifications in a non-compact framework

TL;DR

This paper extends HKKN stratifications to non-compact settings involving vector spaces and Kähler manifolds, and uses these to establish convexity properties of moment maps for invariant subsets.

Contribution

It introduces a new framework for HKKN stratifications in non-compact contexts and applies it to prove convexity of moment maps for certain invariant subsets.

Findings

HKKN stratifications are extended to non-compact Cartesian products.

Convexity properties of the moment map are established for non-compact invariant subsets.

The approach bridges algebraic and analytical methods in symplectic geometry.

Abstract

The aim of this paper is twofold. First, we study HKKN stratifications, both algebraically and analytically, for a Cartesian product between a vector space and a compact K{\"a}hler manifold. We then use these stratifications to prove convexity properties of the moment map for non-compact analytic subsets invariant under a Borel subgroup.