On the Kawamata–Viehweg vanishing theorem for log del Pezzo surfaces in positive characteristic

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...

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Bibliographic Details
Published inCompositio mathematica Vol. 158; no. 4; pp. 750 - 763
Main Authors Arvidsson, Emelie, Bernasconi, Fabio, Lacini, Justin
Format Journal Article
LanguageEnglish
Published London, UK London Mathematical Society 01.04.2022
Cambridge University Press
Subjects
Geometry
Theorems
Kodaira vanishing
14G17
14F17
log del Pezzo surfaces
14E30
14J17
Kawamata log terminal singularities
positive characteristic
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ISSN0010-437X
1570-5846
DOI10.1112/S0010437X22007394

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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 $5$.
Bibliography:ObjectType-Article-1
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ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X22007394