(Uni)rational parametrizations of ℛ g,2 , ℛ g,4  and ℛ g,6  in low genera
[Paramétrisations (uni)rationelles de ℛ g,2 , ℛ g,4 et ℛ g,6 en petits genres]
Knutsen, Andreas Leopold1 ; Lelli-Chiesa, Margherita2 ; Verra, Alessandro2
1Department of Mathematics, University of Bergen, Postboks 7800, 5020 Bergen, Norway
2Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo, 00146 Roma, Italy
Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1411-1440

The moduli space ℛ g,2n parametrizes double covers of smooth curves of genus g ramified at 2n points. We will prove the (uni)rationality of ℛ g,2 , ℛ g,4 and ℛ g,6 in low genera.

L’espace de modules ℛ g,2n paramétrise les revêtements doubles de courbes lisses de genre g ramifiés en 2n points. Nous montrons la (uni)rationalité de ℛ g,2 , ℛ g,4 et ℛ g,6 en petits genres.

Reçu le :
Accepté le :
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DOI : 10.5802/jep.280
Classification : 14H10, 14E08, 14E22, 14J28
Keywords: Prym curves, birational geometry, Nikulin surfaces
Mots-clés : Courbes de Prym, géométrie birationnelle, surfaces de Nikulin

Knutsen, Andreas Leopold  1   ; Lelli-Chiesa, Margherita  2   ; Verra, Alessandro  2

1 Department of Mathematics, University of Bergen, Postboks 7800, 5020 Bergen, Norway
2 Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo, 00146 Roma, Italy
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {(Uni)rational parametrizations of~$\mathcal{R}_{g,2}$,~$\mathcal{R}_{g,4}$~and~$\mathcal{R}_{g,6}$~in~low~genera},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Knutsen, Andreas Leopold; Lelli-Chiesa, Margherita; Verra, Alessandro. (Uni)rational parametrizations of $\mathcal{R}_{g,2}$, $\mathcal{R}_{g,4}$ and $\mathcal{R}_{g,6}$ in low genera. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1411-1440. doi: 10.5802/jep.280

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