On algebraic automorphisms and their rational invariants
| dc.creator | Bonnet, Philippe | |
| dc.date | 2007-04-12 | |
| dc.date.accessioned | 2026-07-07T07:56:20Z | |
| dc.date.available | 2026-07-07T07:56:20Z | |
| dc.description | Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F) be the transcendence degree of k(X)^F over k. In this paper, we study the class of automorphisms F of X for which n(F)= dim X - 1. More precisely, we show that under some conditions on X, every such automorphism is of the form F=A_g, where A is an algebraic action of a linear algebraic group G of dimension 1 on X, and where g belongs to G. As an application, we determine the conjugacy classes of automorphisms of the plane for which n(F)=1. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0704.1588 | |
| dc.identifier | http://arxiv.org/abs/0704.1588 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127275 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14R10, 14R20 | |
| dc.title | On algebraic automorphisms and their rational invariants | |
| dc.type | text |