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arXiv · 1303.5905

A characterization of toric varieties in characteristic p

Piotr Achinger
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Abstract

If $X$ is a smooth toric variety over an algebraically closed field of positive characteristic and $L$ is an invertible sheaf on $X$, it is known that $F_* L$, the push-forward of $L$ along the Frobenius morphism of $X$, is a direct sum of invertible sheaves. We show that this property characterizes smooth projective toric varieties.

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Piotr Achinger. 2013-03-24. A characterization of toric varieties in characteristic p. https://arxiv.org/abs/1303.5905

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