Counterexamples to the Kawamata-Viehweg Vanishing on Ruled Surfaces in Positive Characteristic

2007/02/19 by Qihong Xie, Xie, Qihong
Mathematics · #14E30 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0702554

openalex publication_date 2007/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give counterexamples to the Kawamata-Viehweg vanishing theorem on ruled surfaces in positive characteristic, and prove that if there is a counterexample to the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface f:X-->C, then either C is a Tango curve or all of sections of f are ample.

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