General hyperplane sections of log canonical threefolds in positive characteristic
Algebraic Geometry
2025-09-17 v3 Commutative Algebra
Abstract
In this paper, we prove that if a -dimensional quasi-projective variety over an algebraically closed field of characteristic has only log canonical singularities, then so does a general hyperplane section of . We also show that the same is true for klt singularities, which is a slight extension of \cite{ST20}. 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
Cite
@article{arxiv.2303.14599,
title = {General hyperplane sections of log canonical threefolds in positive characteristic},
author = {Kenta Sato},
journal= {arXiv preprint arXiv:2303.14599},
year = {2025}
}
Comments
27pages, 4figures; v3: added Remark 2.1; simplified the proof of Proposition 3.2; fixed the definition of the node (Definition 3.5); added Remark 3.6 and Lemma 3.7; fixed several typos and minor errors