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arXiv · 2606.09199

Equivariant deformations of isolated singularities and applications

An Khuong Doan
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Abstract

In this paper, we develop an equivariant version of the classical theory of deformations of germs of complex spaces in the presence of complex Lie groups. As a tradition, the main result is the existence of equivariant semi-universal deformations of germs of complex spaces in the reductive case and the non-existence in general in the non-reductive case. The latter is justified by an explicit counterexample. In particular, it generalizes Grauert-Donin's existence theorem to the equivariant settings and Ferrer-Puerta-Slodowy's one to the case of reductive complex Lie groups. Several applications to deformations of pairs, rigidity and actions on Milnor fibers are given.

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An Khuong Doan. 2026-06-08. Equivariant deformations of isolated singularities and applications. https://arxiv.org/abs/2606.09199

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