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Compactifications équivariantes par des courbes. (Equivariant compactifications by curves). (French) Zbl 0626.32031

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 \(\leq 1\). Here, G is a connected complex Lie group and X is normal and irreducible. This generalizes the classification given by A. Huckleberry and 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)].
Reviewer: D.Snow

MSC:

32M10 Homogeneous complex manifolds
32J05 Compactification of analytic spaces
22E10 General properties and structure of complex Lie groups
32M05 Complex Lie groups, group actions on complex spaces
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