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dc.contributor.authorCampillo López, Antonio 
dc.contributor.authorDelgado de la Mata, Félix 
dc.contributor.authorGusein-Zade, Sabir M.
dc.date.accessioned2020-04-14T11:58:38Z
dc.date.available2020-04-14T11:58:38Z
dc.date.issued2020
dc.identifier.citationMathematische Zeitschrift, 2020, vol. 294. p. 593-613es
dc.identifier.issn1432-1823es
dc.identifier.urihttp://uvadoc.uva.es/handle/10324/40736
dc.descriptionProducción Científicaes
dc.description.abstractThe Alexander polynomial in several variables is defined for links in three-dimensional homology spheres, in particular, in the Poincaré sphere: the intersection of the surface S={(z1,z2,z3)∈C3:z51+z32+z23=0} with the 5-dimensional sphere S5ε={(z1,z2,z3)∈C3:|z1|2+|z2|2+|z3|2=ε2}. An algebraic link in the Poincaré sphere is the intersection of a germ of a complex analytic curve in (S, 0) with the sphere S5ε of radius ε small enough. Here we discuss to which extent the Alexander polynomial in several variables of an algebraic link in the Poincaré sphere determines the topology of the link. We show that, if the strict transform of a curve in (S, 0) does not intersect the component of the exceptional divisor corresponding to the end of the longest tail in the corresponding E8-diagram, then its Alexander polynomial determines the combinatorial type of the minimal resolution of the curve and therefore the topology of the corresponding link. The Alexander polynomial of an algebraic link in the Poincaré sphere is determined by the Poincaré series of the filtration defined by the corresponding curve valuations. (They coincide with each other for a reducible curve singularity and differ by the factor (1−t) for an irreducible one.) We show that, under conditions similar to those for curves, the Poincaré series of a collection of divisorial valuations determines the combinatorial type of the minimal resolution of the collection.es
dc.format.mimetypeapplication/pdfes
dc.language.isoenges
dc.publisherSpringeres
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subject.classificationAlgebraic linkses
dc.subject.classificationConexiones algebráicases
dc.subject.classificationPoincaré spherees
dc.subject.classificationEsfera de Poincarées
dc.subject.classificationAlexander polynomiales
dc.subject.classificationPolinomio de Alexanderes
dc.titleAre algebraic links in the Poincaré sphere determined by their Alexander polynomials?es
dc.typeinfo:eu-repo/semantics/articlees
dc.rights.holder© 2020 Springeres
dc.identifier.doi10.1007/s00209-019-02282-0es
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s00209-019-02282-0es
dc.peerreviewedSIes
dc.description.projectMinisterio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant MTM2015-365764-C3-1-P)es
dc.description.projectRussian Science Foundation (grant 16-11-10018)es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersiones


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