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arXiv · 1209.1259

Determining plane curve singularities from its polars

Maria Alberich-Carramiñana·Víctor González-Alonso
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Abstract

This paper addresses a very classical topic that goes back at least to Pl\"ucker: 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.

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Maria Alberich-Carramiñana, Víctor González-Alonso. 2012-09-06. Determining plane curve singularities from its polars. https://arxiv.org/abs/1209.1259

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