Enriched curves and their tropical counterpart
Annales de l'Institut Fourier, Volume 67 (2017) no. 2, p. 689-741

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.

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.

Received : 2015-01-28
Revised : 2016-07-26
Accepted : 2016-09-15
Published online : 2017-05-31
DOI : https://doi.org/10.5802/aif.3095
Classification:  14H10,  14T05
Keywords: Enriched curve, tropical curve, moduli space
     author = {Abreu, Alex C. and Pacini, Marco},
     title = {Enriched curves and their tropical counterpart},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {2},
     year = {2017},
     pages = {689-741},
     doi = {10.5802/aif.3095},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2017__67_2_689_0}
Abreu, Alex C.; Pacini, Marco. Enriched curves and their tropical counterpart. Annales de l'Institut Fourier, Volume 67 (2017) no. 2, pp. 689-741. doi : 10.5802/aif.3095. http://www.numdam.org/item/AIF_2017__67_2_689_0/

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