Open AccessA Gorenstein Criterion for StronglyF-Regular and Log Terminal Singularities
Author(s) -
Anurag K. Singh,
Shunsuke Takagi,
Matteo Varbaro
Publication year - 2016
Publication title -
international mathematics research notices
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.757
H-Index - 76
eISSN - 1687-0247
pISSN - 1073-7928
DOI - 10.1093/imrn/rnw195
Subject(s) - mathematics , conjecture , gravitational singularity , cover (algebra) , singularity , noetherian , pure mathematics , local ring , ring (chemistry) , combinatorics , mathematical analysis , algebra over a field , engineering , mechanical engineering , chemistry , organic chemistry
A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of when a standard graded strongly $F$-regular ring is Gorenstein, in terms of an $F$-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 $F$-pure (resp. log canonical) singularity is quasi-Gorenstein, in terms of an $F$-pure (resp. log canonical) threshold.
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