The unirationality of the Hurwitz schemes H_10,8 and H_13,7

Hanieh Keneshlou (1) , Fabio Tanturri (2)

1 Universität des Saarlandes [Saarbrücken]
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We show that the Hurwitz scheme 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 P^1 × P^2 and P^6 respectively, and through the explicit computation of single examples over a finite field.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Hanieh Keneshlou, Fabio Tanturri. The unirationality of the Hurwitz schemes H_10,8 and H_13,7. Rendiconti Lincei. Matematica e Applicazioni, 2019, 30, pp.31--39. ⟨10.4171/RLM/834⟩. ⟨hal-01663574⟩