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arXiv · 1510.07154

Additive actions on toric varieties

Ivan Arzhantsev·Elena Romaskevich
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Abstract

By an additive action on an algebraic variety $X$ of dimension $n$ we mean a regular action $\mathbb{G}_a^n \times X \to X$ with an open orbit of the commutative unipotent group $\mathbb{G}_a^n$. We prove that if a complete toric variety $X$ admits an additive action, then it admits an additive action normalized by the acting torus. Normalized additive actions on a toric variety $X$ are in bijection with complete collections of Demazure roots of the fan of $X$. Moreover, any two normalized additive actions on $X$ are isomorphic.

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Ivan Arzhantsev, Elena Romaskevich. 2015-10-24. Additive actions on toric varieties. https://doi.org/10.1090/proc%2F13349

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