Analytic extensions of algebraic isomorphisms

S. Kaliman

doi:10.1090/proc/12684

Analytic extensions of algebraic isomorphisms

S. Kaliman

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	4571-4581
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	11
DOIs	https://doi.org/10.1090/proc/12684
State	Published - Nov 1 2015

Keywords

Affine varieties
Group actions
One-parameter subgroups
Transitivity

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AB - 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.

KW - Affine varieties

KW - Group actions

KW - One-parameter subgroups

KW - Transitivity

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

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ER -

Analytic extensions of algebraic isomorphisms

Abstract

Keywords

ASJC Scopus subject areas

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