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arXiv · 1708.08295

Topological invariants of plane curve singularities: Polar quotients and \L ojasiewicz gradient exponents

Hong-Duc Nguyen·Tien-Son Pham·Phi-Dung Hoang
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Abstract

In this paper, we study polar quotients and \L ojasiewicz exponents of plane curve singularities, which are {\em not necessarily reduced}. We first show that the polar quotients is a topological invariant. We next prove that the \L ojasiewicz gradient exponent can be computed in terms of the polar quotients, and so it is also a topological invariant. As an application, we give effective estimates of the \L ojasiewicz exponents in the gradient and classical inequalities of polynomials in two (real or complex) variables.

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Hong-Duc Nguyen, Tien-Son Pham, Phi-Dung Hoang. 2017-08-28. Topological invariants of plane curve singularities: Polar quotients and \L ojasiewicz gradient exponents. https://doi.org/10.1142/s0129167x19500733

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