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Cyclic covers of Stable curves and their moduli spaces
Binru Li1
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, Serie 6, Volume 30 (2021) no. 1, pp. 33-61.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1665
Classification: 14D22, 14H10, 14H15, 32G15
Keywords: Cyclic covering, G-marked stable curves, Boundary of moduli space, Techimüllar space

Binru Li 1

1 Shanghai Center for Mathematicial Sciences, Fudan University. 2005 Songhu road, Yangpu District. 200433 Shanghai, China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Binru Li. Cyclic covers of Stable curves and their moduli spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 1, pp. 33-61. doi : 10.5802/afst.1665. https://afst.centre-mersenne.org/articles/10.5802/afst.1665/

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