dc.contributor.author Nguyen H.D. en_US dc.contributor.author Pham T.-S. en_US dc.contributor.author Hoàng P.-D en_US dc.date.accessioned 2020-03-04T13:44:38Z dc.date.available 2020-03-04T13:44:38Z dc.date.issued 2019-10-21 dc.identifier.uri http://hdl.handle.net/20.500.11824/1094 dc.description.abstract In 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.format application/pdf en_US dc.language.iso eng en_US dc.publisher International Journal of Mathematics en_US dc.relation info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Plane curve singularity, polar curve, polar quotient, Łojasiewicz exponent, Newton polygonNewton–Puiseux root, topological invariant en_US dc.title Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/acceptedVersion en_US dc.identifier.doi https://doi.org/10.1142/S0129167X19500733 dc.relation.publisherversion https://www.worldscientific.com/doi/pdf/10.1142/S0129167X19500733 en_US
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