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Quasi-ordinary singularities and Newton trees

hal.structure.identifierDepartment of mathematics
dc.contributor.authorBARTOLO, E. Artal
hal.structure.identifierDepartment of Algebra
dc.contributor.authorLUENGO, I.
hal.structure.identifierDepartamento de Álgebra [Madrid]
dc.contributor.authorMELLE-HERNÁNDEZ, A.
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCASSOU-NOGUÈS, Pierrette
dc.date.accessioned2024-04-04T03:21:09Z
dc.date.available2024-04-04T03:21:09Z
dc.date.created2012-03-08
dc.date.issued2013
dc.identifier.issn1609-3321
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194641
dc.description.abstractEnIn this paper we study some properties of the class of nu-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasi-ordinary hypersurface singularities among nu-quasi-ordinary hypersurface singularities in terms of their Newton tree. A formula to compute the discriminant of a quasi-ordinary Weierstrass polynomial in terms of the decorations of its Newton tree is given. This allows to compute the discriminant avoiding the use of determinants and even for non Weierstrass prepared polynomials. This is important for applications like algorithmic resolutions. We compare the Newton tree of a quasi-ordinary singularity and those of its curve transversal sections. We show that the Newton trees of the transversal sections do not give the tree of the quasi-ordinary singularity in general. It does if we know that the Newton tree of the quasi-ordinary singularity has only one arrow.
dc.language.isoen
dc.publisherIndependent University of Moscow
dc.title.enQuasi-ordinary singularities and Newton trees
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Géométrie algébrique [math.AG]
dc.identifier.arxiv1203.1704
bordeaux.journalMoscow Mathematical Journal
bordeaux.page365-398
bordeaux.volume13
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01038051
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01038051v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Moscow%20Mathematical%20Journal&rft.date=2013&rft.volume=13&rft.issue=3&rft.spage=365-398&rft.epage=365-398&rft.eissn=1609-3321&rft.issn=1609-3321&rft.au=BARTOLO,%20E.%20Artal&LUENGO,%20I.&MELLE-HERN%C3%81NDEZ,%20A.&CASSOU-NOGU%C3%88S,%20Pierrette&rft.genre=article


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