Discriminant d'un germe $(g, f) : (\mathbb{C}^2,0) \to (\mathbb{C}^2, 0)$ et quotients de contact dans la résolution de $f \cdot g$

Maugendre, Hélène

doi:10.5802/afst.908

Cited by 14 publications

(7 citation statements)

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“…There, he introduced the polar invariants, which in the planar case can be defined from the intersection multiplicity of the whole curve ξ with the branches of a generic polar, and he proved that they are topological invariants of ξ. This result has been generalized by Maugendre in [22] and by Michel in [24], where the role of polars is played by the Jacobian germs of planar morphisms and finite morphisms from normal surface singularities, respectively. The problem of relating a curve to its polars, and vice versa, is the motivation of lots of classical and recent works.…”

Section: Introductionmentioning

confidence: 87%

Determining plane curve singularities from its polars

Alberich-Carramiñana

González-Alonso

2016

Advances in Mathematics

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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.2010 Mathematics Subject Classification (MSC2010): 32S50, 32S15, 14B05.

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