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Unirationality of the Hurwitz space \(\varvec{\mathcal {H}_{9,8}}\)

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Abstract

In this paper we prove that the Hurwitz space \(\mathcal {H}_{9,8}\), which parameterizes 8-sheeted covers of \({\mathbb P }^1\) by curves of genus 9, is unirational. Our construction leads to an explicit Macaulay2 code, which will randomly produce a nodal curve of degree 8 of geometric genus 9 with 12 double points and together with a pencil of degree 8.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran

    Hamid Damadi

  2. Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, 66123, Saarbrücken, Germany

    Frank-Olaf Schreyer

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  1. Hamid Damadi
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  2. Frank-Olaf Schreyer
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Correspondence to Frank-Olaf Schreyer.

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Damadi, H., Schreyer, FO. Unirationality of the Hurwitz space \(\varvec{\mathcal {H}_{9,8}}\) . Arch. Math. 109, 511–519 (2017). https://doi.org/10.1007/s00013-017-1095-3

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