A note on the group extension problem to semi-universal deformation

The aim of this note is twofold. Firstly, we explain in detail Remark 4.1 in Doan (2020) by showing that the action of the automorphism group of the second Hirzebruch surface F2 on itself extends to its formal semi-universal deformation only up to the first order. Secondly, we show that for reductiv...

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Vydáno v:Indagationes mathematicae Ročník 35; číslo 2; s. 240 - 246
Hlavní autor: Doan, An-Khuong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.03.2024
Témata:
Deformation theory
Equivariance structure
Kuranishi family
Moduli theory
Kuranishi family
Equivariance structure
Deformation theory
Moduli theory
ISSN:0019-3577, 1872-6100
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Shrnutí:The aim of this note is twofold. Firstly, we explain in detail Remark 4.1 in Doan (2020) by showing that the action of the automorphism group of the second Hirzebruch surface F2 on itself extends to its formal semi-universal deformation only up to the first order. Secondly, we show that for reductive group actions, the locality of the extended actions on the Kuranishi space constructed in Doan (2021) is the best one could expect in general.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2023.11.003