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

Hanieh Keneshlou, Fabio Tanturri

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 uni…