Quasi-$F$-splitting versus log canonicity

Kenta Sato; Shunsuke Takagi; Shou Yoshikawa

Quasi-$F$-splitting versus log canonicity

Algebraic Geometry 2026-07-02 v1 Commutative Algebra

Authors: Kenta Sato , Shunsuke Takagi , Shou Yoshikawa

Abstract

In this paper, we investigate the relationship between quasi- $F$ -splitting and log canonicity. We show that if a numerically $\mathbb{Q}$ -Gorenstein normal singularity is quasi- $F^e$ -split for every $e\geq 1$ , then it is numerically log canonical. In dimension two, we prove the converse under the condition that the Gorenstein index is not divisible by the characteristic $p$ . We also classify two-dimensional quasi- $F$ -split normal singularities.

Keywords

quasi-F-splitting log canonicity normal singularities Q-Gorenstein characteristic p classification

Cite

@article{arxiv.2607.02218,
  title  = {Quasi-$F$-splitting versus log canonicity},
  author = {Kenta Sato and Shunsuke Takagi and Shou Yoshikawa},
  journal= {arXiv preprint arXiv:2607.02218},
  year   = {2026}
}

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66 pages