## Abstract

Let X′ be a complex affine algebraic threefold with H_{3}(X′) = 0 which is a UFD and whose invertible functions are constants. Let Z be a Zariski open subset of X′ which has a morphism p : Z → U into a curve U such that all fibers of p are isomorphic to C^{2}. We prove that X′ is isomorphic to C^{3} iff none of irreducible components of X′ \ Z has non-isolated singularities. Furthermore, if X′ is C^{3} then p extends to a polynomial on C^{3} which is linear in a suitable coordinate system. This implies the fact formulated in the title of the paper.

Original language | English (US) |
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Pages (from-to) | 161-190 |

Number of pages | 30 |

Journal | Pacific Journal of Mathematics |

Volume | 203 |

Issue number | 1 |

DOIs | |

State | Published - 2002 |

## ASJC Scopus subject areas

- Mathematics(all)

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