### 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) |
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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 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics