no. 6
Moduli of G-covers of curves: geometry and singularities
[Modules de G-recouvrements : géométrie et singularités]
Galeotti, Mattia1
1 Università di Bologna Piazza di Porta S. Donato, 5 40126 Bologna (Italy)
Annales de l'Institut Fourier, Tome 72 (2022) no. 6, pp. 2191-2240.

Nous analysons le lieu singulier et le lieu des singularités non-canoniques de l’espace de modules ℛ ¯ g,G des courbes avec un G-recouvrement où G est un groupe fini. Nous montrons que les singularités non canoniques sont de deux types : T-courbes, c’est-à-dire des singularités relevées de l’espace de modules ℳ ¯ g des courbes stables, et J-courbes, c’est-à-dire des singularités nouvelles caractérisées entièrement par le graphe dual du recouvrement. Enfin, nous prouvons que dans le cas G=S 3 , le lieu J est vide, une première étage très importante dans l’évaluation de la dimension de Kodaira de ℛ ¯ g,S 3

We analyze the singular locus and the locus of non-canonical singularities of the moduli space ℝ ¯ g,G of curves with a G-cover for any finite group G. We show that non-canonical singularities are of two types: T-curves, that is singularities lifted from the moduli space 𝕄 ¯ g of stable curves, and J-curves, that is new singularities entirely characterized by the dual graph of the cover. Finally, we prove that in the case G=S 3 , the J-locus is empty, which is the first fundamental step in evaluating the Kodaira dimension of ℝ ¯ g,S 3 .

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DOI : 10.5802/aif.3503
Classification : 14H10, 14H20, 14H60, 14D20, 14D23
Keywords: Moduli of curves, $G$-covers, curves, stable curves, curve coverings, singularities, birational geometry.
Mot clés : Modules de courbes, $G$-covers, courbes, courbes stables, recouvrements de courbes, singularités, géométrie birationelle.
Galeotti, Mattia 1

1 Università di Bologna Piazza di Porta S. Donato, 5 40126 Bologna (Italy)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Galeotti, Mattia. Moduli of $G$-covers of curves: geometry and singularities. Annales de l'Institut Fourier, Tome 72 (2022) no. 6, pp. 2191-2240. doi : 10.5802/aif.3503. https://aif.centre-mersenne.org/articles/10.5802/aif.3503/

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