A characterization of toric varieties in characteristic p

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 $F_{\ast }L$, 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.

10 pages. Contains arXiv:1012.2021

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