Classification of Kaehler homogeneous manifolds of non-compact dimension two

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Contribution

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Abstract

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup such that $X := G/H$ is Kaehler and the codimension of the top non-vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or equal to two. We show that $X$ is biholomorphic to a complex homogeneous manifold constructed using well-known basic building blocks, i.e., $\mathbb C, \mathbb C^*$, Cousin groups, and flag manifolds.