Additive actions on toric projective hypersurfaces

2020/10/15 by Shafarevich, Anton · 1 citation
#13N15 #14L30 (Primary) 14R20 #14M17 (Secondary) #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.07909

Abstract

Let \mathbbK be an algebraically closed field of characteristic zero and \mathbbG_a be the additive group of \mathbbK. We say that an irreducible algebraic variety X of dimension n over the field \mathbbK admits an additive action if there is a regular action of the group \mathbbG_aⁿ = \mathbbG_a × … × \mathbbG_a (n times) on X with an open orbit. In this paper we find all projective toric hypersurfaces admitting additive action.

Cited by

• Induced additive actions on toric varieties

Related

• Additive actions on complete toric surfaces
• Euler-symmetric projective toric varieties and additive actions
• Additive actions on projective hypersurfaces with a finite number of orbits
• On uniqueness of additive actions on complete toric varieties
• Induced additive actions on toric varieties