Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

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dc.contributor.authorMiranda, A. J.
dc.contributor.authorRizziolli, E. C. [UNESP]
dc.contributor.authorSala, M. J.
dc.contributor.institutionUniversidade Federal de Alfenas (UNIFAL)
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade de São Paulo (USP)
dc.date.accessioned2014-05-27T11:29:05Z
dc.date.available2014-05-27T11:29:05Z
dc.date.issued2013-05-01
dc.description.abstractIn this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.en
dc.description.affiliationDepartamento de Ciências Exatas Universidade Federal de Alfenas, Campus Alfenas, Rua Gabriel Monteiro da Silva, n: 700, 37130-000, Alfenas, M.G
dc.description.affiliationDepartamento de Matemática Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista 'Júlio Mesquita Filho', Campus de Rio Claro, Caixa Postal 178, 13506-700 Rio Claro SP
dc.description.affiliationDepartamento de Matemática Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo - Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP
dc.description.affiliationUnespDepartamento de Matemática Instituto de Geociências e Ciências Exatas Universidade Estadual Paulista 'Júlio Mesquita Filho', Campus de Rio Claro, Caixa Postal 178, 13506-700 Rio Claro SP
dc.format.extent189-222
dc.identifierhttp://www.rc.unesp.br/igce/matematica/rpsilva/pre-prints/pre-prints/Pre-print_files/ECRizziolliRevised17-05-2012.pdf
dc.identifier.citationJP Journal of Geometry and Topology, v. 13, n. 2, p. 189-222, 2013.
dc.identifier.issn0972-415X
dc.identifier.lattes9873188602749310
dc.identifier.scopus2-s2.0-84878975555
dc.identifier.urihttp://hdl.handle.net/11449/75331
dc.language.isoeng
dc.relation.ispartofJP Journal of Geometry and Topology
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectGeometry of quasi homogeneous map germs
dc.subjectInvariants of stable singularities
dc.titleStable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3en
dc.typeArtigo
unesp.author.lattes9873188602749310
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Geociências e Ciências Exatas, Rio Claropt

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