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dc.contributor.authorNguyen H.D.en_US
dc.contributor.authorPham T.-S.en_US
dc.contributor.authorHoàng P.-Den_US
dc.date.accessioned2020-03-04T13:44:38Z
dc.date.available2020-03-04T13:44:38Z
dc.date.issued2019-10-21
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1094
dc.description.abstractIn this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a topological invariant. We next prove that the Łojasiewicz gradient exponent can be computed in terms of the polar quotients, and so it is also a topological invariant. For real plane curve singularities, we also give a formula computing the Łojasiewicz gradient exponent via real polar branches. As an application, we give effective estimates of the Łojasiewicz exponents in the gradient and classical inequalities of polynomials in two (real or complex) variables.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherInternational Journal of Mathematicsen_US
dc.relationinfo:eu-repo/grantAgreement/EC/FP7/615655en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectPlane curve singularity, polar curve, polar quotient, Łojasiewicz exponent, Newton polygonNewton–Puiseux root, topological invarianten_US
dc.titleTopological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponentsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/acceptedVersionen_US
dc.identifier.doihttps://doi.org/10.1142/S0129167X19500733
dc.relation.publisherversionhttps://www.worldscientific.com/doi/pdf/10.1142/S0129167X19500733en_US


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