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

Access to Document

10.1090/proc/12684

Cite this

@article{b824189cf2ad493fbe6735e82243c9e9,

title = "Analytic extensions of algebraic isomorphisms",

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.",

keywords = "Affine varieties, Group actions, One-parameter subgroups, Transitivity",

author = "S. Kaliman",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2015",

month = nov,

day = "1",

doi = "10.1090/proc/12684",

language = "English (US)",

volume = "143",

pages = "4571--4581",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "11",

}

TY - JOUR

T1 - Analytic extensions of algebraic isomorphisms

AU - Kaliman, S.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84940398873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940398873&partnerID=8YFLogxK

U2 - 10.1090/proc/12684

DO - 10.1090/proc/12684

M3 - Article

AN - SCOPUS:84940398873

VL - 143

SP - 4571

EP - 4581

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -

Analytic extensions of algebraic isomorphisms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this