dc.contributor.author Sampaio, J.E. dc.date.accessioned 2019-01-05T15:33:27Z dc.date.available 2019-01-05T15:33:27Z dc.date.issued 2018-08-14 dc.identifier.issn 0002-9939 dc.identifier.uri http://hdl.handle.net/20.500.11824/905 dc.description.abstract We 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.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Bi-Lipschitz contact at infinity en_US dc.subject Zariski's Conjecture en_US dc.subject Degree en_US dc.title On Zariski’s multiplicity problem at infinity en_US dc.type info:eu-repo/semantics/doctoralThesis en_US dc.identifier.arxiv 1709.03373 dc.relation.publisherversion https://doi.org/10.1090/proc/14432 en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Proceedings of the American Mathematical Society en_US
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