F-jumping and F-Jacobian ideals for hypersurfaces

• Luis Núñez-Betancourt ^[1] ; Felipe Pérez ^[2]
  1. [1] University of Virginia

     University of Virginia

     Estados Unidos

     
  2. [2] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 220, Nº 1 (January 2016), 2016, págs. 292-318
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.06.012
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• Resumen

  • We introduce two families of ideals, F-jumping ideals and F-Jacobian ideals, in order to study the singularities of hypersurfaces in positive characteristic. Both families are defined using the D -modules MαMα that were introduced by Blickle, Mustaţă and Smith. Using strong connections between F-jumping ideals and generalized test ideals, we give a characterization of F-jumping numbers for hypersurfaces via D-modules and F-modules. In addition, we use F-Jacobian ideals to study intrinsic properties of the singularities of hypersurfaces. In particular, we give conditions for F-regularity. Moreover, we prove several properties of F-Jacobian ideals that resemble those of Jacobian ideals of polynomials.