arXiv math/06103112006-10math.CVmath.DG

Proper actions of high-dimensional groups on complex manifolds

A. V. Isaev

备注：: 29 pages

英文摘要：

We explicitly classify all pairs $(M,G)$, where $M$ is a connected complex manifold of dimension $n\ge 2$ and $G$ is a connected Lie group acting properly and effectively on $M$ by holomorphic transformations and having dimension $d_G$ satisfying $n^2+2\le d_G<n^2+2n$. These results extend -- in the complex case -- the classical description of manifolds admitting proper actions of groups of sufficiently high dimensions. They also generalize some of the author's earlier work on Kobayashi-hyperbolic manifolds with high-dimensional holomorphic automorphism group.

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