6533b85bfe1ef96bd12bb6fc
RESEARCH PRODUCT
Rationally integrable vector fields and rational additive group actions
Alvaro LiendoAdrien Duboulozsubject
Integrable systemRationally integrable derivationsGeneral Mathematics010102 general mathematics05 social sciencesLocally nilpotentAlgebraic variety01 natural sciencesLocally nilpotent derivations[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]AlgebraHomogeneousRational additive group actions0502 economics and businessVector fieldAffine transformation[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]050207 economics0101 mathematicsInvariant (mathematics)MSC: 14E07 14L30 14M25 14R20Additive groupMathematicsdescription
International audience; 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-07-01 |