Rationality of some projective linear actions

Abstract

Let K be any field which may not be algebraically closed, V a finite-dimensional vector space over K, σ∈GL(V) where the order of σ can be finite or infinite. Theorem.If dimKV≤3, then both K(V)〈σ〉 and K(P(V))〈σ〉 are rational (=purely transcendental) over K. Similar results hold for a cyclic affine action. © 2000 Academic Press.