(Uni)rational parametrizations of $\mathcal{R}_{g,2}$, $\mathcal{R}_{g,4}$ and $\mathcal{R}_{g,6}$ in low genera

Andreas Leopold Knutsen; Margherita Lelli-Chiesa; Alessandro Verra

doi:10.5802/jep.280

(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]

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

Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1411-1440.

Résumé
Abstract

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

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

Reçu le : 2023-12-22
Accepté le : 2024-10-30
Publié le : 2024-11-06

DOI : 10.5802/jep.280

Classification : 14H10, 14E08, 14E22, 14J28
Keywords: Prym curves, birational geometry, Nikulin surfaces
Mot clés : Courbes de Prym, géométrie birationnelle, surfaces de Nikulin

Affiliations des auteurs :

Andreas Leopold Knutsen ¹ ; Margherita Lelli-Chiesa ² ; Alessandro Verra 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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     author = {Andreas Leopold Knutsen and Margherita Lelli-Chiesa and Alessandro Verra},
     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},
     pages = {1411--1440},
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     year = {2024},
     doi = {10.5802/jep.280},
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}

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Andreas Leopold Knutsen; Margherita Lelli-Chiesa; Alessandro Verra. (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. https://jep.centre-mersenne.org/articles/10.5802/jep.280/

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