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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.
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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