Analytic extensions of algebraic isomorphisms

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Abstract

Let Ψ : X1 → X2 be an isomorphism of closed affine algebraic subvarieties of ℂn such that n > max(2 dimX1, dimTX1). We prove that Ψ can be extended to a holomorphic automorphism of ℂn. Furthermore, when Ψ is an isomorphism of curves, such an extension exists for every n ≥ 3 even when dim TX1 = n.

Original languageEnglish (US)
Pages (from-to)4571-4581
Number of pages11
JournalProceedings of the American Mathematical Society
Volume143
Issue number11
DOIs
StatePublished - Nov 1 2015

Keywords

  • Affine varieties
  • Group actions
  • One-parameter subgroups
  • Transitivity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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