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dc.contributor.authorSampaio J. E.en_US
dc.date.accessioned2019-01-05T15:33:27Z
dc.date.available2019-01-05T15:33:27Z
dc.date.issued2018-08-14
dc.identifier.issn0002-9939
dc.identifier.urihttp://hdl.handle.net/20.500.11824/905
dc.description.abstractWe address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, we prove that the degree is a bi-Lipschitz invariant at infinity when the bi-Lipschitz homeomorphism has Lipschitz constants close to 1. In particular, we have that a family of complex algebraic sets bi-Lipschitz equisingular at infinity has constant degree. Moreover, we prove that if two polynomials are weakly rugose equivalent at infinity, then they have the same degree. In particular, we obtain that if two polynomials are rugose equivalent at infinity or bi-Lipschitz contact equivalent at infinity or bi-Lipschitz right-left equivalent at infinity, then they have the same degree.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherProceedings of the American Mathematical Societyen_US
dc.relationinfo:eu-repo/grantAgreement/EC/FP7/615655en_US
dc.relationES/1PE/SEV-2013-0323en_US
dc.relationEUS/BERC/BERC.2014-2017en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectBi-Lipschitz contact at infinityen_US
dc.subjectZariski's Conjectureen_US
dc.subjectDegreeen_US
dc.titleOn Zariski’s multiplicity problem at infinityen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/publishedVersionen_US
dc.identifier.arxiv1709.03373
dc.relation.publisherversionhttps://doi.org/10.1090/proc/14432en_US


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