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

epiga:4486 - Épijournal de Géométrie Algébrique, November 9, 2018, Volume 2 - https://doi.org/10.46298/epiga.2018.volume2.4486
Hamiltonian actions of unipotent groups on compact Kähler manifoldsArticle

Authors: Daniel Greb ; Christian Miebach

    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.

    Volume: Volume 2
    Published on: November 9, 2018
    Accepted 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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