# Extensions of isomorphisms of subvarieties in flexile varieties

## TL;DR

This paper investigates conditions under which isomorphisms between subvarieties of certain flexible quasi-affine varieties can be extended to automorphisms of the entire variety, enhancing understanding of their automorphism groups.

## Contribution

It provides new criteria for extending subvariety isomorphisms to automorphisms in flexible quasi-affine varieties, expanding the theory of automorphism groups.

## Key findings

- Identifies conditions for extension of isomorphisms to automorphisms.
- Focuses on varieties complementing low-dimensional subvarieties in complex affine space.
- Contributes to the understanding of automorphism groups of flexible varieties.

## Abstract

Let $X$ be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most $n-3$ in $\C^n$. We find some conditions under which an isomorphism of two closed subvarieties of $X$ can be extended to an automorphism of $X$.