Additive actions on toric varieties

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.

14 pages. arXiv admin note: text overlap with arXiv:1104.0560 by other authors

References in corpus (1)

• Uniqueness of equivariant compactifications of C^n by a Fano manifold of Picard number 1

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