Stacky Hamiltonian Actions and Symplectic Reduction

We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer–Marsden–Weinstein symplectic reduction theorem, and the Duistermaat–Heckman theorem in this context.

Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable K\"ahler structures obtained by symplectic reduction. The relation of our complex-analytic theory to the work of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group actions on projective varieties is discussed in detail. Comment: v2: 30 pages, final version as accepted by EPIGA