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arXiv · 2607.02218

Quasi-$F$-splitting versus log canonicity

Kenta Sato·Shunsuke Takagi·Shou Yoshikawa
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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.

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Kenta Sato, Shunsuke Takagi, Shou Yoshikawa. 2026-07-02. Quasi-$F$-splitting versus log canonicity. https://arxiv.org/abs/2607.02218

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