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PreprintarXiv licencearXiv

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 ℚ-Gorenstein normal singularity is quasi-Fe-split for every e≥ 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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Cite

BibTeXRIS
BibTeX
@misc{sato2026quasifsplitting,
  title = {{Quasi-$F$-splitting versus log canonicity}},
  author = {Kenta Sato and Shunsuke Takagi and Shou Yoshikawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.02218},
  eprint = {2607.02218},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.02218},
}
RIS
TY  - UNPB
TI  - Quasi-F-splitting versus log canonicity
AU  - Kenta Sato
AU  - Shunsuke Takagi
AU  - Shou Yoshikawa
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2607.02218
UR  - https://arxiv.org/abs/2607.02218
AB  - In this paper, we investigate the relationship between quasi-F-splitting and log canonicity. We show that if a numerically ℚ-Gorenstein normal singularity is quasi-F^e-split for every e≥ 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.
ER  -