Hamiltonian actions of unipotent groups on compact K\"ahler manifolds
Complex Variables
2023-06-22 v2 Algebraic Geometry
Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1805.02551,
title = {Hamiltonian actions of unipotent groups on compact K\"ahler manifolds},
author = {Daniel Greb and Christian Miebach},
journal= {arXiv preprint arXiv:1805.02551},
year = {2023}
}
Comments
v2: 30 pages, final version as accepted by EPIGA