Geodesic
On Complex Homogeneous Spaces with Top Homology in Codimension Two
Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 897-919

Voir la notice de l'article provenant de la source Cambridge University Press

Define dx to be the codimension of the top nonvanishing homologygroup of the manifold X with coefficients in 2. We investigate homogeneous spaces X := G/H, where G is a connected complex Lie group and H is a closed complex subgroup for which dx = 1,2 and O(X) ≠ C. There exists a fibration π: G/H → G/U such that G/U is holomorphically separable and π*(O(G/U)) = O(G/H), see [11]. We prove the following. If dx = 1, then F := U/H is compact and connected and Y :=G/U is an affine cone with its vertex removed. If dx = 2, then either F is connected with dF = 1 and Y is an affine cone with its vertex removed, or F is compact and connected and dy = 2, where Y is C, the affine quadric Q2, P2 — Q (with Q a quadric curve) or a homogeneous holomorphic * -bundle over an affine cone minus its vertex which is itself an algebraic principal bundle or which admits a two-to-one covering that is.
DOI : 10.4153/CJM-1994-051-x
Mots-clés : 32M10 
Akhiezer, D. N.; Gilligan, B. On Complex Homogeneous Spaces with Top Homology in Codimension Two. Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 897-919. doi: 10.4153/CJM-1994-051-x
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