Publication

Determining plane curve singularities from its polars

Journal Article (2016)

Journal

Advances in Mathematics

Pages

788-822

Volume

287

Number

1

Doc link

http://dx.doi.org/10.1016/j.aim.2015.10.011

File

Download the digital copy of the doc pdf document

Authors

Abstract

This paper addresses a very classical topic that goes back at least to Plücker: how to understand a plane curve singularity using its polar curves. Here, we explicitly construct the singular points of a plane curve singularity directly from the weighted cluster of base points of its polars. In particular, we determine the equisingularity class (or topological equivalence class) of a germ of plane curve from the equisingularity class of generic polars and combinatorial data about the non-singular points shared by them.

Categories

pattern recognition.

Author keywords

Germ of plane curve; Polar; Equisingularity; Topological equivalence; Enriques diagram

Scientific reference

M. Alberich-Carramiñana and V. González-Alonso. Determining plane curve singularities from its polars. Advances in Mathematics , 287(1): 788-822, 2016.