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NON-LOG LIFTABLE LOG DEL PEZZO SURFACES OF RANK ONE IN CHARACTERISTIC FIVE

Part of: Families, fibrations Surfaces and higher-dimensional varieties Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  10 February 2025

MASARU NAGAOKA Open the ORCID record for MASARU NAGAOKA [Opens in a new window]
MASARU NAGAOKA*
Affiliation:
Department of Mathematics Gakushuin University 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588 Japan masaru.nagaoka@gakushuin.ac.jp
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Abstract

Building upon the classification by Lacini, we determine the isomorphism classes of log del Pezzo surfaces of rank one over an algebraically closed field of characteristic five either which are not log liftable over the ring of Witt vectors or whose singularities are not feasible in characteristic zero. We also show that such a surface is always constructed from the Du Val del Pezzo surface of Dynkin type $2[2^4]$. Furthermore, We show that the Kawamata–Viehweg vanishing theorem for ample $\mathbb {Z}$-Weil divisors holds for log del Pezzo surfaces of rank one in characteristic five if those singularities are feasible in characteristic zero.

Keywords

log del Pezzo surfacesliftability to the ring of Witt vectorspositive characteristic

MSC classification

Primary: 14J26: Rational and ruled surfaces 14D15: Formal methods; deformations
Secondary: 14G17: Positive characteristic ground fields 14J45: Fano varieties

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 259 , September 2025 , pp. 399 - 422
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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