Plane algebraic curves of arbitrary genus via Heegaard Floer homology

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https://doi.org/10.4171/cmh/411

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2017-05-22

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https://hdl.handle.net/2022/32903

Abstract

Suppose C is a singular curve in CP2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots Ki. We apply Heegaard Floer theory to find new constraints on the sets of knots {Ki} 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, d>33, that possess exactly one singularity which has exactly one Puiseux pair (p;q). The realized triples (p,d,q) are expressed as successive even terms in the Fibonacci sequence.

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This record is for a(n) offprint of an article published in Math.Helvetici on 2017-05-22; the version of record is available at https://doi.org/10.4171/cmh/411.

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Borodzik, Maciej, et al. "Plane algebraic curves of arbitrary genus via Heegaard Floer homology." Math.Helvetici, vol. 92, 2017-5-22, https://doi.org/10.4171/cmh/411.

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Math.Helvetici

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