Abstract
A compact complex manifoldX is an equivariant compactification of a homogeneous manifoldG/H (G a connected complex Lie group,H a closed complex subgroup ofG), if there exists a holomorphic action ofG onX such that theG-orbit of some pointx inX is open and H is the isotropy group ofx. GivenG andH, for some groups (e.g.,G nilpotent) there are necessary and sufficient conditions for the existence of an equivariant Kähler compactification which are proven in this paper.
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Massmann, B. Equivariant Kähler compactifications of homogeneous manifolds. J Geom Anal 2, 555–574 (1992). https://doi.org/10.1007/BF02921577
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DOI: https://doi.org/10.1007/BF02921577