Plane algebraic curves of arbitrary genus via Heegaard Floer homology

  • Maciej Borodzik

    University of Warsaw, Poland
  • Matthew Hedden

    Michigan State University, East Lansing, USA
  • Charles Livingston

    Indiana University, Bloomington, USA

Abstract

Suppose is a singular curve in and it is topologically an embedded surface of genus ; such curves are called cuspidal. The singularities of are cones on knots . We apply Heegaard Floer theory to find new constraints on the sets of knots that can arise as the links of singularities of cuspidal curves. We combine algebro-geometric constraints with ours to solve the existence problem for curves with genus one, , that possess exactly one singularity which has exactly one Puiseux pair . The realized triples are expressed as successive even terms in the Fibonacci sequence.

Cite this article

Maciej Borodzik, Matthew Hedden, Charles Livingston, Plane algebraic curves of arbitrary genus via Heegaard Floer homology. Comment. Math. Helv. 92 (2017), no. 2, pp. 215–256

DOI 10.4171/CMH/411