# A counter-example to the equivariance structure on semi-universal deformation

## TL;DR

This paper presents a counter-example demonstrating that a $G$-equivariant extension does not always exist on the formal semi-universal deformation of a projective variety with an algebraic group action.

## Contribution

It provides the first known counter-example to the presumed equivariance structure on semi-universal deformations of algebraic varieties.

## Key findings

- Counter-example to $G$-equivariant extensions established
- Shows limitations of equivariance in deformation theory
- Highlights need for revised understanding of deformation structures

## Abstract

If $X$ is a projective variety and $G$ is an algebraic group acting algebraically on $X$, we provide a counter-example to the existence of a $G$-equivariant extension on the formal semi-universal deformation of $X$.