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arXiv · 0911.1110

Ga-actions of fiber type on affine T-varieties

Alvaro Liendo
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Abstract

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.

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Alvaro Liendo. 2009-11-05. Ga-actions of fiber type on affine T-varieties. https://doi.org/10.1016/j.jalgebra.2010.09.008

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