Heegaard Floer homology and rational cuspidal curves

Abstract

We apply the methods of Heegaard Floer homology to identify topological properties of complex curves in the complex projective plane. As one application, we resolve an open conjecture that constrains the Alexander polynomial of the link of the singular point of the curve in the case that there is exactly one singular point, having connected link, and the curve is of genus 0. Generalizations apply in the case of multiple singular points.

18 pages

References in corpus (3)

• Floer homology and knot complements
• On knot Floer homology and cabling II
• On the knot Floer filtration of the concordance group

Cited by in corpus (21)

• The reduced knot Floer complex
• The Coolidge-Nagata conjecture
• A note on cobordisms of algebraic knots
• Cuspidal curves and Heegaard Floer homology
• Cuspidal curves, minimal models and Zaidenberg's finiteness conjecture
• Dehn surgeries and rational homology balls
• Semigroups, d-invariants and deformations of cuspidal singular points of plane curves
• Classification of planar rational cuspidal curves. I. C**-fibrations
• A restriction on the Alexander polynomials of $L$-space knots
• Involutive Heegaard Floer homology and rational cuspidal curves
• The trace embedding lemma and spinelessness
• On sums of torus knots concordant to alternating knots
• Using secondary Upsilon invariants to rule out stable equivalence of knot complexes
• On the First Singularity for the Upsilon Invariant of Algebraic Knots
• On independence of iterated Whitehead doubles in the knot concordance group
• Topological obstructions for rational cuspidal curves in Hirzebruch surfaces
• On the secondary Upsilon invariant
• On the nonorientable four-ball genus of torus knots
• New family of hyperbolic knots whose Upsilon invariants are convex
• Heegaard Floer homology and plane curves with non-cuspidal singularities
• Classification of rational unicuspidal curves with two Newton pairs