Analytic extensions of algebraic isomorphisms

Abstract

Let $\Psi :X_1\to X_2$ be an isomorphism of closed affine algebraic subvarities of $\C^n$ such that $n>\max (2\dim X_1,\dim T{X}_1)$. We prove that $\Psi$ can be extended to a holomorphic automorphism of $\C^n$. Furthermore, when $\Psi$ is an isomorphism of curves such an extension exists for every $n\ge 3$ even when $\dim T{X}_1=n$.

11 pages

References in corpus (1)

• The Gromov-Winkelmann theorem for flexible varieties

Cited by in corpus (2)

• Lagrangian embeddings of cubic fourfolds containing a plane
• Holomorphically Equivalent Algebraic Embeddings