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

@article{Keneshlou2017TheUO,
  title={The unirationality of the Hurwitz schemes \$\mathcal H_\{10, 8\}\$ and \$\mathcal H_\{13, 7\}\$},
  author={H. Keneshlou and Fabio Tanturri},
  journal={Rendiconti Lincei-matematica E Applicazioni},
  year={2017},
  volume={30},
  pages={31-39}
}
  • H. Keneshlou, Fabio Tanturri
  • Published 2017
  • Mathematics
  • Rendiconti Lincei-matematica E Applicazioni
  • 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. 

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