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arXiv · 1409.3282

Cuspidal curves and Heegaard Floer homology

József Bodnár·Daniele Celoria·Marco Golla
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Abstract

We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux pair: we prove two identities tying the parameters of the singularity, the genus, and the degree of the curve; we improve on some degree-multiplicity asymptotic inequalities; finally, we prove some finiteness results, we construct infinite families of examples, and in some cases we give an almost complete classification.

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József Bodnár, Daniele Celoria, Marco Golla. 2015-12-01. Cuspidal curves and Heegaard Floer homology. https://doi.org/10.1112/plms%2Fpdv074

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