Additive Actions on Toric Projective Hypersurfaces

Abstract

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