Abstract

Let X be a normal affine T-variety where T stands for the algebraic torus We classify G(a)-actions on X arising from homogeneous locally nilpotent derivations of fiber type We deduce that any variety with trivial Makar-Limanov (ML) invariant is birationally decomposable as Y x P-2 for some Y Conversely given a variety Y there exists an affine variety X with trivial ML invariant birational to Y x P-2 Finally we introduce a new version of the ML invariant called the FML invariant According to our conjecture the triviality of the FML invariant implies rationality We confirm this conjecture in dimension at most 3 (C) 2010 Elsevier Inc All rights reserved