Ga-actions of fiber type on affine T-varieties

Alvaro Liendo (1)

1 IF - Institut Fourier

Let X be a normal affine T-variety, where T stands for the algebraic torus. We classify Ga-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\times P^2, for some Y. Conversely, given a variety Y, there exists an affine variety X with trivial ML invariant birational to Y\times 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. This conjecture holds in dimension at most 3.

Mots clés: Torus action; Ga-action; locally nilpotent derivations; affine varieties; Makar-Limanov invariant

Domaines: Géométrie algébrique [math.AG]

Alvaro Liendo. Ga-actions of fiber type on affine T-varieties. 2009. ⟨hal-00430172⟩