A characterization of toric varieties in characteristic p

Piotr Achinger

A characterization of toric varieties in characteristic p

Algebraic Geometry 2013-03-26 v1

Authors: Piotr Achinger

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.

Keywords

toric varieties characteristic p frobenius morphism invertible sheaves algebraic geometry projective varieties

Cite

@article{arxiv.1303.5905,
  title  = {A characterization of toric varieties in characteristic p},
  author = {Piotr Achinger},
  journal= {arXiv preprint arXiv:1303.5905},
  year   = {2013}
}

Comments

10 pages. Contains arXiv:1012.2021

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