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Journal Articles Mathematische Annalen Year : 2011

Homogeneous Kähler and Hamiltonian manifolds

Abstract

We consider actions of reductive complex Lie groups $G=K^C$ on Kähler manifolds $X$ such that the $K$--action is Hamiltonian and prove then that the closures of the $G$--orbits are complex-analytic in $X$. This is used to characterize reductive homogeneous Kähler manifolds in terms of their isotropy subgroups. Moreover we show that such manifolds admit $K$--moment maps if and only if their isotropy groups are algebraic.
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Dates and versions

hal-00445106 , version 1 (07-01-2010)
hal-00445106 , version 2 (02-06-2010)

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Bruce Gilligan, Christian Miebach, Karl Oeljeklaus. Homogeneous Kähler and Hamiltonian manifolds. Mathematische Annalen, 2011, 349 (4), pp.889-901. ⟨10.1007/s00208-010-0546-y⟩. ⟨hal-00445106v2⟩
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