Parametrization simple irreducible plane curve singularities in arbitrary characteristic

2019/01/09 by Hồng Đức Nguyễn, Nguyen, Hong-Duc · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1901.02758

openalex publication_date 2019/01/09 · openalex created_date 2019/01/25 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Curvature criteria of A-simple singularities R,0-> R²,0 and their parallel curves

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• Curvature criteria of A-simple singularities R,0-> R²,0 and their parallel curves