Greb, Daniel; Miebach, Christian Hamiltonian actions of unipotent groups on compact Kähler manifolds. (Actions hamiltoniennes des groupes unipotents sur les variétés kälériennes compactes.) (English. French summary) Zbl 1408.32022 Épijournal de Géom. Algébr., EPIGA 2, Article No. 10, 30 p. (2018). Summary: We study meromorphic actions of unipotent complex Lie groups on compact Kähler 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 Kähler 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. Cited in 2 Documents MSC: 32M05 Complex Lie groups, group actions on complex spaces 32M10 Homogeneous complex manifolds 32J27 Compact Kähler manifolds: generalizations, classification Keywords:unipotent complex Lie groups; automorphisms of compact Kähler manifolds PDFBibTeX XMLCite \textit{D. Greb} and \textit{C. Miebach}, Épijournal de Géom. Algébr., EPIGA 2, Article No. 10, 30 p. (2018; Zbl 1408.32022) Full Text: arXiv Link