The unirationality of the Hurwitz schemes $\mathcal H_{10, 8}$ and $\mathcal H_{13, 7}$

Keneshlou, Hanieh; Tanturri, Fabio

doi:10.4171/RLM/834

Rendiconti Lincei - Matematica e Applicazioni

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Volume 30, Issue 1, 2019, pp. 31–39

DOI: 10.4171/RLM/834

Published online: 2019-04-01

The unirationality of the Hurwitz schemes $\mathcal H_{10, 8}$ and $\mathcal H_{13, 7}$

Hanieh Keneshlou and Fabio Tanturri^[1]

(1) Université de Lille, Villeneuve-d'Ascq, France

We show that the Hurwitz scheme $\mathcal{H}_{g,d}$ parametrizing $d$-sheeted simply branched covers of the projective line by smooth curves of genus $g$, up to isomorphism, is unirational for $(g,d)=(10,8)$ and $(13,7)$. The unirationality is settled by using liaison constructions in $\mathbb{P}^1 \times \mathbb{P}^2$ and $\mathbb{P}^6$ respectively, and through the explicit computation of single examples over a finite field.

Keywords: Hurwitz spaces, moduli spaces of curves, unirationality, linkage

Keneshlou Hanieh, Tanturri Fabio: The unirationality of the Hurwitz schemes $\mathcal H_{10, 8}$ and $\mathcal H_{13, 7}$. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), 31-39. doi: 10.4171/RLM/834