On rational additive group actions
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.
Cite
@article{arxiv.1409.5878,
title = {On rational additive group actions},
author = {Adrien Dubouloz and Alvaro Liendo},
journal= {arXiv preprint arXiv:1409.5878},
year = {2014}
}