Additive actions on toric projective hypersurfaces

Abstract

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