A note on the group extension problem to semi-universal deformation
Abstract
The aim of this note is twofold. Firstly, we explain in detail Remark 4.1 in doan-a 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-equivariant is the best one could expect in general.
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