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GENERAL HYPERPLANE SECTIONS OF LOG CANONICAL THREEFOLDS IN POSITIVE CHARACTERISTIC

Part of: Surfaces and higher-dimensional varieties Local theory

Published online by Cambridge University Press:  14 April 2025

Kenta Sato Open the ORCID record for Kenta Sato [Opens in a new window]
Kenta Sato*
Affiliation:
Department of Mathematics and Informatics, Chiba University, 1-33, Yayoicho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan
*
sato@math.s.chiba-u.ac.jp
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Abstract

In this paper, we prove that if a three-dimensional quasi-projective variety X over an algebraically closed field of characteristic $p>3$ has only log canonical singularities, then so does a general hyperplane section H of X. We also show that the same is true for klt singularities, which is a slight extension of [15]. In the course of the proof, we provide a sufficient condition for log canonical (resp. klt) surface singularities to be geometrically log canonical (resp. geometrically klt) over a field.

Keywords

Bertini theoremgeometrically log canonical singularitiessurface singularitiesdual graph

MSC classification

Primary: 14B05: Singularities
Secondary: 14J17: Singularities

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , First View , pp. 1 - 28
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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