Enriched curves and their tropical counterpart
[Courbes enrichies et leur analogue tropical]
Annales de l'Institut Fourier, Tome 67 (2017) no. 2, pp. 689-741.

Dans sa thèse, Mainò a introduit la notion de structure enrichie sur les courbes stables et elle a construit leur espace des modules. Dans cet article, nous donnons une notion tropicale de structure enrichie sur les courbes tropicales et nous construisons un espace de modules qui paramètre ces objets. De plus, nous utilisons cette construction pour donner une description torique du schéma qui paramètre les structures enrichies sur une courbe stable fixée.

In her Ph.D. thesis, Mainò introduced the notion of enriched structure on stable curves and constructed their moduli space. In this paper we give a tropical notion of enriched structure on tropical curves and construct a moduli space parametrizing these objects. Moreover, we use this construction to give a toric description of the scheme parametrizing enriched structures on a fixed stable curve.

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DOI : 10.5802/aif.3095
Classification : 14H10, 14T05
Keywords: Enriched curve, tropical curve, moduli space
Mot clés : Courbe enrichie, courbe tropicale, espace de modules
Abreu, Alex C. 1 ; Pacini, Marco 1

1 Universidade Federal Fluminense Instituto de Matemática Rua M. S. Braga, s/n, Valonguinho Niterói, RJ 24020-140 (Brazil)
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Abreu, Alex C.; Pacini, Marco. Enriched curves and their tropical counterpart. Annales de l'Institut Fourier, Tome 67 (2017) no. 2, pp. 689-741. doi : 10.5802/aif.3095. http://archive.numdam.org/articles/10.5802/aif.3095/

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