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Equivariant Kuranishi family of complex compact manifolds

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Abstract

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.

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Acknowledgements

This is a part of my Ph.D thesis at Institut de mathém-atiques de Jussieu—Paris Rive Gauche (IMJ-PRG). I would like to profoundly thank my thesis advisor—Prof. Julien Grivaux for many precious discussions, for his enthusiastic instructions, his continuous support, his extremely careful reading and his comments, which help enormously to establish this work. I am warmly grateful to the referee whose work led to a considerable improvement of the paper.

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  1. IMJ-PRG, UMR 7586, Sorbonne Université, Case 247, 4 Place Jussieu, 75252, Paris Cedex 05, France

    An-Khuong Doan

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Correspondence to An-Khuong Doan.

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Doan, AK. Equivariant Kuranishi family of complex compact manifolds. manuscripta math. 167, 793–808 (2022). https://doi.org/10.1007/s00229-021-01289-4

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  • DOI: https://doi.org/10.1007/s00229-021-01289-4

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