Greb, Daniel and Miebach, Christian - Hamiltonian actions of unipotent groups on compact Kähler manifolds

epiga:4486 - Épijournal de Géométrie Algébrique, November 9, 2018, Volume 2
Hamiltonian actions of unipotent groups on compact Kähler manifolds

Authors: Greb, Daniel and Miebach, Christian

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.


Source : oai:arXiv.org:1805.02551
Volume: Volume 2
Published on: November 9, 2018
Submitted on: May 8, 2018
Keywords: Mathematics - Complex Variables,Mathematics - Algebraic Geometry,Mathematics - Differential Geometry,32M05, 32M10, 32Q15, 14L24, 14L30, 37J15, 53D20


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