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Journal Articles Épijournal de Géométrie Algébrique Year : 2018

Hamiltonian actions of unipotent groups on compact Kähler manifolds

Daniel Greb
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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. Comment: v2: 30 pages, final version as accepted by EPIGA
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Dates and versions

hal-03600379 , version 1 (07-03-2022)

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Daniel Greb, Christian Miebach. Hamiltonian actions of unipotent groups on compact Kähler manifolds. Épijournal de Géométrie Algébrique, 2018, 2, ⟨10.46298/epiga.2018.volume2.4486⟩. ⟨hal-03600379⟩
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