We prove that actions of complex reductive Lie groups on a complex compact manifold are locally extendable to its Kuranishi family. This can be seen as an analogue of Rim’s result (see Rim in Trans Am Math Soc 257(1):217–226, 1980) in the analytic setting.

中文翻译：

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等变Kuranishi系列复杂紧凑流形

我们证明了在复杂紧流形上的复杂还原李群的作用在本地可扩展至其Kuranishi家族。在分析环境中，这可以看作是Rim结果的类似物（请参见Trans Am Math Soc 257（1）：217-226，1980中的Rim）。