紧K\ ahler流形上幂偶群的哈密顿作用

IF 0.9 Q2 MATHEMATICS Epijournal de Geometrie Algebrique Pub Date : 2018-05-07 DOI:10.46298/epiga.2018.volume2.4486

D. Greb, C. Miebach

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引用次数: 2

摘要

利用矩映射技术研究了紧阿勒流形上单幂复李群的亚纯作用。引入自然稳定条件，证明了半稳定点集是zariski -开和容许的几何商，它们携带由辛约化得到的可紧化K\ ahler结构。详细讨论了复解析理论与Doran—Kirwan关于射影变簇上单幂群的几何不变理论的关系。评论:v2: 30页，最终版本被EPIGA接受

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Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

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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