Cuspidal curves and Heegaard Floer homology

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.

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

References in corpus (1)

• Floer homology and knot complements

Cited by in corpus (8)

• A note on cobordisms of algebraic knots
• Dehn surgeries and rational homology balls
• Topological obstructions for rational cuspidal curves in Hirzebruch surfaces
• Analytic lattice cohomology of surface singularities
• Rational cuspidal curves and symplectic fillings
• Heegaard Floer homology and plane curves with non-cuspidal singularities
• Analytic lattice cohomology of surface singularities, II (the equivariant case)
• The analytic lattice cohomology of isolated singularities