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Zbl 0626.32031
Lescure, François
Compactifications équivariantes par des courbes. (Equivariant compactifications by curves). (French)
[J] Mém. Soc. Math. Fr., Nouv. Sér. 26, 91 p. (1987). ISSN 0249-633X

In this memoire, the author classifies the equivariant compactifications of a homogeneous space $\Omega =G/H$ to a compact complex space X such that the complement $X\setminus \Omega$ has complex dimension $\le 1$. Here, G is a connected complex Lie group and X is normal and irreducible. This generalizes the classification given by {\it A. Huckleberry} and {\it E. Oeljeklaus} for the case where X is non-singular [see `Classification theorems for almost-homogeneous spaces' (1984; Zbl 0549.32024)], announced in C. R. Acad. Sci., Paris, Sér. A 290, 447-448 (1980; Zbl 0444.32015)].
[D.Snow]

MSC 2000:: *32M10 Homogeneous complex manifolds
32J05 Compactification of analytic spaces
22E10 General properties and structure of complex Lie groups
32M05 Automorphism groups of complex spaces

Keywords: equivariant compactifications of a homogeneous space

Citations: Zbl 0549.32024; Zbl 0444.32015

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