Cyclic covers of Stable curves and their moduli spaces

Binru Li

doi:10.5802/afst.1665

Binru Li ¹

¹ Shanghai Center for Mathematicial Sciences, Fudan University. 2005 Songhu road, Yangpu District. 200433 Shanghai, China

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 1, pp. 33-61.

Résumé
Abstract

Nous étudions la déformation des courbes stables marquées de $G$ dans le cas où $G$ est un groupe cyclique et construisons un espace de paramétrage pour les courbes stables marquées par $G$ d’un type numérique donné.

Ceci est ensuite utilisé afin d’étudier les composantes de l’ensemble des courbes stables en admettant l’action d’un groupe cyclique de non-premier ordre $d$ , extension du travail de F. Catanese dans le cas où $d$ est premier.

We study the deformation of $G$ -marked stable curves in the case where $G$ is a cyclic group, and construct a parameterizing space for $G$ -marked stable curves of a given numerical type.

This is then used in order to study the components of the locus of stable curves admitting the action of a cyclic group of non prime order $d$ , extending the work of F. Catanese in the case where $d$ is prime.

Reçu le : 2018-01-12
Accepté le : 2019-05-27
Publié le : 2021-05-25

DOI : 10.5802/afst.1665

Classification : 14D22, 14H10, 14H15, 32G15
Mots clés : Cyclic covering, G-marked stable curves, Boundary of moduli space, Techimüllar space

Affiliations des auteurs :

Binru Li ¹

¹ Shanghai Center for Mathematicial Sciences, Fudan University. 2005 Songhu road, Yangpu District. 200433 Shanghai, China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Binru Li. Cyclic covers of Stable curves and their moduli spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 1, pp. 33-61. doi : 10.5802/afst.1665. https://afst.centre-mersenne.org/articles/10.5802/afst.1665/

Bibliographie
Cité par

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