  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.
