### Abstract

Let Ψ : X_{1} → X_{2} be an isomorphism of closed affine algebraic subvarieties of ℂ^{n} such that n > max(2 dimX_{1}, dimTX_{1}). We prove that Ψ can be extended to a holomorphic automorphism of ℂ^{n}. Furthermore, when Ψ is an isomorphism of curves, such an extension exists for every n ≥ 3 even when dim TX_{1} = 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 | |

State | Published - Nov 1 2015 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Analytic extensions of algebraic isomorphisms.** / Kaliman, Shulim.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 143, no. 11, pp. 4571-4581. https://doi.org/10.1090/proc/12684

}

TY - JOUR

T1 - Analytic extensions of algebraic isomorphisms

AU - Kaliman, Shulim

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 -