Cuspidal curves and Heegaard Floer homology
Geometric Topology
2017-05-17 v3
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.
Keywords
Cite
@article{arxiv.1409.3282,
title = {Cuspidal curves and Heegaard Floer homology},
author = {József Bodnár and Daniele Celoria and Marco Golla},
journal= {arXiv preprint arXiv:1409.3282},
year = {2017}
}
Comments
39 pages, 4 figures. Exposition improved. This preprint version differs from the final version which is to appear in the Proceedings of the London Mathematical Society