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On the Kawamata-Viehweg vanishing theorem for log del Pezzo surfaces in positive characteristic. (English) Zbl 1489.14024

Summary: We prove the Kawamata-Viehweg vanishing theorem for surfaces of del Pezzo type over perfect fields of positive characteristic \(p>5\). As a consequence, we show that klt threefold singularities over a perfect base field of characteristic \(p>5\) are rational. We show that these theorems are sharp by providing counterexamples in characteristic \(5\).

MSC:

14E30 Minimal model program (Mori theory, extremal rays)
14F17 Vanishing theorems in algebraic geometry
14G17 Positive characteristic ground fields in algebraic geometry
14J17 Singularities of surfaces or higher-dimensional varieties
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