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A Counter-Example to the Equivariance Structure on Semi-universal Deformation

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Abstract

If X is a projective variety and G is an algebraic group acting algebraically on X, we provide a counter-example to the existence of a G-equivariant extension on the formal semi-universal deformation of X.

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Acknowledgements

I would like to thank Prof. Bernd Siebert for many useful discussions. Actually, I learned the idea of using the extension of vector fields and their relations as obstructions to the extension of the group action from an unpublished paper of his. This provides a strategy to attack the problem. I am specially thankful to Prof. Julien Grivaux for his careful reading and his comments which help to improve the manuscript. Finally, I am warmly grateful to the referee whose work led to a remarkable 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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  1. An Khuong Doan
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Correspondence to An Khuong Doan.

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Doan, A.K. A Counter-Example to the Equivariance Structure on Semi-universal Deformation. J Geom Anal 31, 3698–3712 (2021). https://doi.org/10.1007/s12220-020-00411-4

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  • DOI: https://doi.org/10.1007/s12220-020-00411-4

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