Determining plane curve singularities from its polars
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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.
CitationGonzález-Alonso, V., Alberich, M. Determining plane curve singularities from its polars. "Advances in mathematics", 10 Gener 2016, vol. 287, p. 788.