Gupta, Neena
(2014)
*On the family of affine threefolds x ^{m}y=F(x,z,t)*
Compositio Mathematica, 150
(6).
pp. 979-998.
ISSN 0010-437X

Full text not available from this repository.

Official URL: http://doi.org/10.1112/S0010437X13007793

Related URL: http://dx.doi.org/10.1112/S0010437X13007793

## Abstract

Let k be a field and V the affine threefold in A4k defined by xmy=F(x,z,t), m⩾2. In this paper, we show that V≅A3k if and only if f(z,t):=F(0,z,t) is a coordinate of k[z,t]. In particular, when k is a field of positive characteristic and f defines a non-trivial line in the affine plane A2k (we shall call such a V as an Asanuma threefold), then V≆A3k although V×A1k≅A4k, thereby providing a family of counter-examples to Zariski’s cancellation conjecture for the affine 3-space in positive characteristic. Our main result also proves a special case of the embedding conjecture of Abhyankar–Sathaye in arbitrary characteristic.

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to London Mathematical Society. |

Keywords: | Polynomial Algebra; Graded Ring; Ga-action;Derksen Invariant; Makar-Limanov Invariant; Cancellation Problem; Embedding Problem; A2-Fibration, Localization Theorem Of K-Theory. |

ID Code: | 121186 |

Deposited On: | 12 Jul 2021 12:37 |

Last Modified: | 12 Jul 2021 12:37 |

Repository Staff Only: item control page