Publication:
Nash multiplicity sequences and Hironaka's order function

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorBravo, Ana
dc.contributor.authorPascual Escudero, Beatriz
dc.contributor.authorEncinas, S.
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2022-01-27T11:22:56Z
dc.date.available2022-01-27T11:22:56Z
dc.date.issued2020
dc.description.abstractWhen X is a d-dimensional variety defined over a field k of characteristic zero, a constructive resolution of singularities can be achieved by successively lowering the maximum multiplicity via blow ups at smooth equimultiple centers. This is done by stratifying the maximum multiplicity locus of X by means of the so called resolution functions. The most important of these functions is what we know as Hironaka’s order function in dimension d. Actually, this function can be defined for varieties when the base field is perfect; however if the characteristic of k is positive, the function is, in general, too coarse and does not provide enough information so as to define a resolution. It is very natural to ask what the meaning of this function is in this case, and to try to find refinements that could lead, ultimately, to a resolution. In this paper we show that Hironaka’s order function in dimension d can be read in terms of the Nash multiplicity sequences introduced by Lejeune-Jalabert. Therefore, the function is intrinsic to the variety and has a geometrical meaning in terms of its space of arcs.en
dc.description.sponsorshipThe authors were partially supported by MTM2015-68524-P. The third author was supported by BES-2013-062656.en
dc.format.extent41
dc.identifier.bibliographicCitationBravo, A., Pascual-Escudero, B. & Encinas, S. (2020). Nash multiplicity sequences and Hironaka’s order function. Indiana University Mathematics Journal, 69(6), 1933–1973.en
dc.identifier.doihttps://doi.org/10.1512/iumj.2020.69.8016
dc.identifier.issn0022-2518
dc.identifier.publicationfirstpage1933
dc.identifier.publicationissue6
dc.identifier.publicationlastpage1973
dc.identifier.publicationtitleIndiana University Mathematics Journalen
dc.identifier.publicationvolume69
dc.identifier.urihttps://hdl.handle.net/10016/33982
dc.identifier.uxxiAR/0000027903
dc.language.isoengen
dc.publisherIndiana University Mathematics Journalen
dc.relation.projectIDGobierno de España. MTM2015-68524-Pes
dc.relation.projectIDGobierno de España. BES-2013-062656es
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherRees algebrasen
dc.subject.otherResolution of singularitiesen
dc.subject.otherArc spacesen
dc.titleNash multiplicity sequences and Hironaka's order functionen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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