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Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities

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arxiv math/0006124 v1 pith:TEVYFWHA submitted 2000-06-18 math.AG math.GT

Norbert A'Campo This is my paper · ORCID
classification math.AGmath.GT
keywords monodromygeometricreductioncurvecurvescyclesgroupplane
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The geometric monodromy of a plane curve singularity is a quasi-finite diffeomorphism. In this paper we locate the reduction curves of the geometric monodromy and the quadratic vanishing cycles of the singularity. An application to the geometric monodromy group is given.

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  1. Real morsifications via the trace map

    math.AG 2026-08 accept novelty 8.0 of 10

    Every reduced real plane curve singularity is shown to admit a real morsification, via a new trace map built from nodal smoothings of normalization disks.

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