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

Qihong Xie
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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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Qihong Xie. 2007-02-19. Counterexamples to the Kawamata-Viehweg Vanishing on Ruled Surfaces in Positive Characteristic. https://arxiv.org/abs/math/0702554

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