arXiv subjects

Hong-Duc Nguyen

Publications and source records attributed to Hong-Duc Nguyen.

2 recordsLinked to original sources

arXiv2019

Parametrization simple irreducible plane curve singularities in arbitrary characteristic

We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its conductor. Then we classify parametrization simple plane curve singularities which are irreducible by giving a concrete list of normal forms of equations and parametrizations. In characteristic zero, the classification of parametrization simple irreducible plane curve singularities was achieved by Bruce and Gaffney.

math.AG↗

arXiv2017

Topological invariants of plane curve singularities: Polar quotients and Łojasiewicz gradient exponents

In this paper, we study polar quotients and Łojasiewicz 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 Łojasiewicz 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 Łojasiewicz exponents in the gradient and classical inequalities of polynomials in two (real or complex) variables.

math.AG↗