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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Bibliographic Details
Published in:Indagationes mathematicae Vol. 35; no. 2; pp. 240 - 246
Main Author: Doan, An-Khuong
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2024
Subjects:
Deformation theory
Equivariance structure
Kuranishi family
Moduli theory
Kuranishi family
Equivariance structure
Deformation theory
Moduli theory
ISSN:0019-3577, 1872-6100
Online Access:Get full text
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Summary: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