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