English

A Gorenstein criterion for strongly $F$-regular and log terminal singularities

Commutative Algebra 2024-05-21 v3 Algebraic Geometry

Abstract

A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of when a standard graded strongly FF-regular ring is Gorenstein, in terms of an FF-pure threshold. We prove this conjecture under the additional hypothesis that the anti-canonical cover of the ring is Noetherian. Moreover, under this hypothesis on the anti-canonical cover, we give a similar criterion for when a normal FF-pure (resp. log canonical) singularity is quasi-Gorenstein, in terms of an FF-pure (resp. log canonical) threshold.

Keywords

Cite

@article{arxiv.1603.08422,
  title  = {A Gorenstein criterion for strongly $F$-regular and log terminal singularities},
  author = {Anurag K. Singh and Shunsuke Takagi and Matteo Varbaro},
  journal= {arXiv preprint arXiv:1603.08422},
  year   = {2024}
}

Comments

This version corrects some errors in Proposition 4.9, Remark 4.10, and Proposition 4.13; the main theorems stay the same