Hilbert–Kunz multiplicities and F-thresholds

  • Luis Núñez-BetancourtEmail author
  • Ilya Smirnov
Original Article


Motivated by relations between Hilbert–Samuel multiplicity and F-thresholds, we conjecture an inequality that relates F-thresholds with Hilbert–Kunz multiplicity. In this article, we present several results that support the conjecture. In particular, we prove it for hypersurfaces and we give several consequences of this inequality. In addition, we extend previous results for the Hilbert–Samuel multiplicity.

Mathematics Subject Classification

Primary 13D40 13A35 14B05 



We would like to thank Craig Huneke for valuable discussions. L. Núñez-Betancourt was supported by the NSF Grant DMS 1502282 and the CONACyT (Mexico) Grant \(\#284598.\) I. Smirnov was partially supported by NSF Grant DMS 1259142. We also thank the referee for helpful comments.


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Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Centro de Investigación en MatemáticasGuanajuatoMexico
  2. 2.Department of MathematicsStockholm UniversityStockholmSweden

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