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Topology of hypersurface singularities

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arxiv 1706.04386 v1 pith:G6IVDDUB submitted 2017-06-14 math.AG

Topology of hypersurface singularities

classification math.AG
keywords singularitiesahlereinerhypersurfacetopologyalgebraischenanderlichenaren
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K\"ahler's paper "\"Uber die Verzweigung einer algebraischen Funktion zweier Ver\"anderlichen in der Umgebung einer singul\"aren Stelle" offered a more perceptual view of the link of a complex plane curve singularity than that provided shortly before by Brauner. K\"ahler's innovation of using a "square sphere" became standard in the toolkit of later researchers on singularities. We describe his contribution and survey developments since then, including a brief discussion of the topology of isolated hypersurface singularities in higher dimension.

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  1. Instanton slices and their superpolynomials

    math.AG 2026-07 conditional novelty 7.0

    Motivic superpolynomials of plane-curve singularities are repackaged as "instanton slice" counts, conjecturally matching new DAHA superpolynomials that are claimed to produce superpolynomials for hyperbolic knots.