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arXiv · 2108.04041

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

An Khuong Doan
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Abstract

The aim of this note is twofold. Firstly, we explain in detail Remark 4.1 in \cite{doan-a} by showing that the action of the automorphism group of the second Hirzebruch surface $\mathbb{F}_2$ 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 \cite{doan-equivariant} is the best one could expect in general.

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An Khuong Doan. 2021-08-09. A note on the group extension problem to semi-universal deformation. https://doi.org/10.1016/j.indag.2023.11.003

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