A characterization of toric varieties in characteristic p

2013/03/24 by Piotr Achinger, Achinger, Piotr · 4 citations
Mathematics · #14g17 #14m25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1303.5905

openalex publication_date 2013/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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