Complex Manifolds Admitting Proper Actions of High-Dimensional Groups

A. Isaev

Journal of Lie theory, Tome 18 (2008) no. 1, pp. 141-16

Résumé

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 $n^2+2\le d_G$. We also consider the case $d_G=n^2+1$. In this case all actions split into three types according to the form of the linear isotropy subgroup. We give a complete explicit description of all pairs $(M,G)$ for two of these types, as well as a large number of examples of actions of the third type. These results complement a theorem due to W. Kaup for the maximal group dimension $n^2+2n$ and generalize some of the author's earlier work on Kobayashi-hyperbolic manifolds with high-dimensional holomorphic automorphism group.

Détail

Classification : 53C30, 32M10, 32Q57
Mots-clés : Proper group actions, complex manifolds