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On the Kawamata–Viehweg vanishing theorem for log del Pezzo surfaces in positive characteristic
Part of
Emelie Arvidsson, Fabio Bernasconi, Justin Lacini
Journal:

Compositio Mathematica / Volume 158 / Issue 4 / April 2022

Published online by Cambridge University Press:

13 June 2022, pp. 750-763

Print publication:

April 2022
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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 $5$.