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F-thresholds of graded rings
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: Nagoya mathematical journal, ISSN 0027-7630, E-ISSN 2152-6842, Vol. 229, p. 141-168Article in journal (Refereed) Published
Abstract [en]

The a-invariant, the F-pure threshold, and the diagonal Fthreshold are three important invariants of a graded K-algebra. Hirose, Watanabe, and Yoshida have conjectured relations among these invariants for strongly F-regular rings. In this article, we prove that these relations hold only assuming that the algebra is F-pure. In addition, we present an interpretation of the a-invariant for F-pure Gorenstein graded K-algebras in terms of regular sequences that preserve F-purity. This result is in the spirit of Bertini theorems for projective varieties. Moreover, we show connections with projective dimension, Castelnuovo–Mumford regularity, and Serre’s condition Sk. We also present analogous results and questions in characteristic zero. 

Place, publisher, year, edition, pages
Cambridge University Press, 2018. Vol. 229, p. 141-168
Keywords [en]
A-invariant, Castelnuovo–Mumford regularity, Diagonal F-threshold, F-pure threshold, F-purity, Projective dimension
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-227424DOI: 10.1017/nmj.2016.65ISI: 000440465600006Scopus ID: 2-s2.0-85041838955OAI: oai:DiVA.org:kth-227424DiVA, id: diva2:1210587
Note

QC 20180529

Available from: 2018-05-29 Created: 2018-05-29 Last updated: 2018-10-08Bibliographically approved

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