Additive actions on toric varieties

Arzhantsev, Ivan; Romaskevich, Elena

doi:10.1090/proc/13349

Additive actions on toric varieties
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by Ivan Arzhantsev and Elena Romaskevich PDF

Proc. Amer. Math. Soc. 145 (2017), 1865-1879 Request permission

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 $\Sigma _X$. Moreover, any two normalized additive actions on $X$ are isomorphic.

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