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On log del Pezzo surfaces in large characteristic

Part of: (Co)homology theory General commutative ring theory Birational geometry

Published online by Cambridge University Press:  08 March 2017

Paolo Cascini ,
Hiromu Tanaka  and
Jakub Witaszek
Paolo Cascini
Affiliation:
Department of Mathematics, Imperial College, London, 180 Queen’s Gate, London SW7 2AZ, UK email p.cascini@imperial.ac.uk
Hiromu Tanaka
Affiliation:
Department of Mathematics, Imperial College, London, 180 Queen’s Gate, London SW7 2AZ, UK email h.tanaka@imperial.ac.uk
Jakub Witaszek
Affiliation:
Department of Mathematics, Imperial College, London, 180 Queen’s Gate, London SW7 2AZ, UK email j.witaszek14@imperial.ac.uk
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Abstract

We show that any Kawamata log terminal del Pezzo surface over an algebraically closed field of large characteristic is globally $F$-regular or it admits a log resolution which lifts to characteristic zero. As a consequence, we prove the Kawamata–Viehweg vanishing theorem for klt del Pezzo surfaces of large characteristic.

Keywords

log del Pezzo surfaceF-singularitiesKawamata–Viehweg vanishingpositive characteristic

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays) 14F17: Vanishing theorems 13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 4 , April 2017 , pp. 820 - 850
Copyright
© The Authors 2017 

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