Extensions of isomorphisms of subvarieties in flexile 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 $X$.

arXiv commentIn this version (March 2018) there are new sections with extra results about the extension problem in SL(n). In version 3 add two sections 8 and 9 concerning the extension problem for affine quadrics and SL (n). The first seven sections are essentially the same. In version 4 there are small corrections in Proposition 6.7 and Remark 6.8

References in corpus (1)

• Criteria for the density property of complex manifolds