Convexity properties for generalized moment maps I

TL;DR

This paper investigates convexity and connectedness properties of generalized moment maps in the context of Hamiltonian torus actions on compact twisted generalized complex manifolds, extending classical symplectic results.

Contribution

It proves convexity and connectedness of generalized moment maps for Hamiltonian torus actions on twisted generalized complex manifolds, building on Lin and Tolman's framework.

Findings

Convexity of the generalized moment map image

Connectedness of the fibers of the moment map

Extension of classical convexity theorems to generalized complex geometry

Abstract

We study generalized moment maps for a Hamiltonian action on a connected compact $H$-twisted generalized complex manifold introduced by Lin and Tolman and prove the convexity and connectedness properties of the generalized moment maps for a Hamiltonian torus action.