Rationally integrable vector fields and 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. Our results lead 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 counterpart of the Makar-Limanov invariant for affine varieties and describe the structure of rational homogeneous additive group actions on toric varieties.
Type de document :
Article dans une revue
International Journal of Mathematics, World Scientific Publishing, 2016, 27 (8), pp. 1650060 <http://www.worldscientific.com/doi/abs/10.1142/S0129167X16500609?journalCode=ijm>. <10.1142/S0129167X16500609 >
Liste complète des métadonnées

https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01407992
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 2 décembre 2016 - 19:16:31
Dernière modification le : mardi 7 février 2017 - 11:58:28

Identifiants

Collections

Citation

Adrien Dubouloz, Alvaro Liendo. Rationally integrable vector fields and rational additive group actions. International Journal of Mathematics, World Scientific Publishing, 2016, 27 (8), pp. 1650060 <http://www.worldscientific.com/doi/abs/10.1142/S0129167X16500609?journalCode=ijm>. <10.1142/S0129167X16500609 >. <hal-01407992>

Partager

Métriques

Consultations de la notice

35