F-jumping and F-Jacobian ideals for hypersurfaces

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• 作者：Luis Nú ; ñ ; ez-Betancourt^a ; ^{lcn8m@virginia.edu" class="auth_mail" title="E-mail the corresponding author} ; Felipe Pé ; rez^b ; ^{juanfp@umich.edu" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：220
• 期：1
• 页码：292-318
• 全文大小：610 K

文摘

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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915001802&_mathId=si1.gif&_user=111111111&_pii=S0022404915001802&_rdoc=1&_issn=00224049&md5=50d9f62e0af8bd5a1ee71f03b07d10c2" title="Click to view the MathML source">M_伪class="mathContainer hidden">class="mathCode">$M_{伪}$ that were introduced by Blickle, Musta牛膬 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.