Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 4

Special Issue: In Honor of Prof. Gert-Martin Greuel’s 75th Birthday

Guest Editors: Igor Burban, Stanislaw Janeczko, Gerhard Pfister, Stephen S.T. Yau, and Huaiqing Zuo

Parametrization simple irreducible curve singularities in arbitrary characteristic

Pages: 1053 – 1066

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n4.a6

Author

Hong Duc Nguyen (Basque Center for Applied Mathematics, Bilbao, Bizkaia, Spain; and TIMAS, Thang Long University, Nghiem Xuan Yem, Hanoi, Vietnam)

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. We then define the notion of parametrization modality for plane curve singularities. Finally, we re-visit Mehmood–Pfister’s classification of 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.

Received 2 January 2019

Accepted 11 December 2019

Published 13 November 2020