On rational additive group actions

Adrien Dubouloz; Alvaro Liendo

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arXiv · 1409.5878

On rational additive group actions

Adrien Dubouloz·Alvaro Liendo

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Abstract

We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. This leads in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counter-part of the Makar-Limanov invariant for affine varieties and describe the structure of rational homogeneous additive group actions on toric varieties.

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Adrien Dubouloz, Alvaro Liendo. 2014-09-20. On rational additive group actions. https://arxiv.org/abs/1409.5878

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