On proper actions of Lie groups of dimension n2+1 on n-dimensional complex manifolds
- Isaev, A.V.
DOIAbstract
AbstractWe explicitly classify all pairs (M,G), where M is a connected complex manifold of dimension n⩾2 and G is a connected Lie group acting properly and effectively on M by holomorphic transformations and having dimension dG satisfying n2+2⩽dG<n2+2n. We also consider the case dG=n2+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 n2+2n and generalize some of the author's earlier work on Kobayashi-hyperbolic manifolds with high-dimensional holomorphic au...
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