On algebraic automorphisms and their rational invariants

Details On algebraic automorphisms and their rational invariants On algebraic automorphisms and their rational invariants

2007-04-12

arxiv.org/abs/0704.1588v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On algebraic automorphisms and their rational invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On algebraic automorphisms and their rational invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On algebraic automorphisms and their rational invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-148050