Proper actions of Lie groups of dimension $n^2+1$ on $n$-dimensional complex manifolds

Details Proper actions of Lie groups of dimension $n^2+1$ on $n$-dimensional complex manifolds Proper actions of Lie groups of dimension $n^2+1$ on $n$-dimensional complex manifolds

2007-11-14

arxiv.org/abs/0711.2098v1

Mathematics

Complex Variables

60 pages

Scientific paper

In this paper we continue to study actions of high-dimensional Lie groups on complex manifolds. We give a complete explicit description of all pairs $(M,G)$, where $M$ is a connected complex manifold $M$ of dimension $n\ge 2$, and $G$ is a connected Lie group of dimension $n^2+1$ acting effectively and properly on $M$ by holomorphic transformations. This result complements a classification obtained earlier by the first author for $n^2+2\le\hbox{dim} G

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