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.

中文翻译：

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复曲面投影超曲面上的加法作用

设\({{\mathbb {K}}}\)是特征为零的代数闭域，而\({{\mathbb {G}}}_a\)是\({{\mathbb {K} }}}\)。我们说一个不可约代数簇X维的Ñ在字段\（{{\ mathbb {K}}} \）如果存在的基团的常规操作承认添加剂动作\（{{\ mathbb {G}} }_a^n = {{\mathbb {G}}}_a \times \cdots \times {{\mathbb {G}}}_a\)（n次）在X 上，具有开放的轨道。在本文中，我们发现所有允许加性作用的射影复曲面超曲面。