Kaliman, Shulim and Vénéreau, Stéphane and Zaidenberg, Mihail.
(2004)
* Simple birational extensions of the polynomial algebra ℂ³.*
Transactions of the American Mathematical Society, Vol. 356, H. 2.
pp. 509-555.

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Official URL: http://edoc.unibas.ch/dok/A5253592

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## Abstract

The Abhyankar-Sathaye Problem asks wether any biregular embeddingof Ck into Cn can be rectified. Here we studythis problem for the embeddings of C3 into C4 whose image X isgiven in C4 by an equation p = f(x; y)u+g(x; y; z) = 0. Under certain additional assumptions we show that, indeed,the polynomial p is a variable of the polynomial ring C[4] = C[x; y; z; u] (i.e., acoordinate of a polynomial automorphism of C4). This is an analog of a theoremdue to Sathaye (1976) which concerns the case of embeddings of C2 into C3.Besides, we generalize a theorem of Miyanishi (1984) giving, for a polynomialp as above, a criterion for when X is isomorphic to C3.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft) |
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UniBasel Contributors: | Vénéreau, Stéphane |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Johns Hopkins Univ. Press |

ISSN: | 0002-9947 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Last Modified: | 22 Mar 2012 14:27 |

Deposited On: | 22 Mar 2012 13:58 |

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