Heegaard Floer homology, knotifications of links, and plane curves with noncuspidal singularities

We describe a formula for the H 1 -action on the knot Floer homology of knotifications of links in S 3 .Using our results about knotifications, we are able to study complex curves with noncuspidal singularities, which were inaccessible using previous Heegaard Floer techniques.We focus on the case of a transverse double point, and give examples of complex curves of genus g which cannot be topologically deformed into a genus g 1 surface with a single double point.14H50; 14B05, 57K18, 57R58 1. Introduction 4837 2. Review of Heegaard Floer theory 4842 3. Correction terms 4857 4. Staircase complexes and their tensor products 4860 5. Topology of complex curves and their neighborhoods 4872 6. Nonrational noncuspidal complex curves 4878