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 -regular ring is Gorenstein, in terms of an -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 -pure (resp. log canonical) singularity is quasi-Gorenstein, in terms of an -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