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Transactions of the American Mathematical Society

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On the existence of $ F$-thresholds and related limits

Authors: Alessandro De Stefani, Luis Núñez-Betancourt and Felipe Pérez
Journal: Trans. Amer. Math. Soc. 370 (2018), 6629-6650
MSC (2010): Primary 13A35; Secondary 13D45, 14B05
Published electronically: March 19, 2018
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We show the existence of $ F$-thresholds in full generality. In addition, we study properties of standard graded algebras over a field for which $ F$-pure threshold and $ F$-threshold at the irrelevant maximal ideal agree. We also exhibit explicit bounds for the $ a$-invariants and Castelnuovo-Mumford regularity of Frobenius powers of ideals in terms of $ F$-thresholds and $ F$-pure thresholds, obtaining the existence of related limits in certain cases.

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Additional Information

Alessandro De Stefani
Affiliation: Department of Mathematics, Royal Institute of Technology (KTH), 100 44 Stockholm, Sweden
Address at time of publication: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130

Luis Núñez-Betancourt
Affiliation: Centro de Investigación en Matemáticas, Guanajuato, GTO, México

Felipe Pérez
Affiliation: Department of Mathematics & Statistics, Georgia State University, Atlanta, Georgia 30303

Keywords: $F$-thresholds, $a$-invariants, $F$-pure thresholds, Castelnuovo-Mumford regularity, strong $F$-regularity, $F$-signature.
Received by editor(s): May 11, 2016
Received by editor(s) in revised form: December 24, 2016
Published electronically: March 19, 2018
Additional Notes: The second author was partially supported by NSF Grant 1502282.
Dedicated: Dedicated to Professor Craig Huneke on the occasion of his sixty-fifth birthday
Article copyright: © Copyright 2018 American Mathematical Society

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