Geodesic
Hamiltonian actions of unipotent groups on compact Kähler manifolds
Épijournal de Géométrie Algébrique, Tome 2 (2018)

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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. 
@article{10_46298_epiga_2018_volume2_4486,
     author = {Greb, Daniel and Miebach, Christian},
     title = {Hamiltonian actions of unipotent groups on compact {K\"ahler} manifolds},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {2},
     year = {2018},
     doi = {10.46298/epiga.2018.volume2.4486},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2018.volume2.4486/}
}
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Greb, Daniel; Miebach, Christian. Hamiltonian actions of unipotent groups on compact Kähler manifolds. Épijournal de Géométrie Algébrique, Tome 2 (2018). doi: 10.46298/epiga.2018.volume2.4486

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