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.
Revised:
Accepted:
Published online:
Keywords: Enriched curve, tropical curve, moduli space
Mot clés : Courbe enrichie, courbe tropicale, espace de modules
Abreu, Alex C. 1; Pacini, Marco 1
@article{AIF_2017__67_2_689_0, author = {Abreu, Alex C. and Pacini, Marco}, title = {Enriched curves and their tropical counterpart}, journal = {Annales de l'Institut Fourier}, pages = {689--741}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {67}, number = {2}, year = {2017}, doi = {10.5802/aif.3095}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3095/} }
TY - JOUR AU - Abreu, Alex C. AU - Pacini, Marco TI - Enriched curves and their tropical counterpart JO - Annales de l'Institut Fourier PY - 2017 SP - 689 EP - 741 VL - 67 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3095/ DO - 10.5802/aif.3095 LA - en ID - AIF_2017__67_2_689_0 ER -
%0 Journal Article %A Abreu, Alex C. %A Pacini, Marco %T Enriched curves and their tropical counterpart %J Annales de l'Institut Fourier %D 2017 %P 689-741 %V 67 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3095/ %R 10.5802/aif.3095 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.3095/
[1] The tropicalization of the moduli space of curves, Ann. Sci. Éc. Norm. Supér., Volume 48 (2015) no. 4, pp. 765-809 | DOI
[2] Riemann–Roch theory for weighted graphs and tropical curves, Adv. Math., Volume 240 (2013), pp. 1-23 | DOI
[3] Geometry of algebraic curves, Volume II, Grundlehren der Mathematischen Wissenschaften, 268, Springer, 2011, xxii+928 pages (With a contribution by J. Harris.)
[4] Riemann–Roch and Abel–Jacobi theory on a finite graph, Adv. Math., Volume 215 (2007) no. 2, pp. 766-788 | DOI
[5] The functor of toric varieties associated with Weyl chambers and Losev–Manin moduli spaces, Tohoku Math. J., Volume 63 (2011) no. 4, pp. 581-604 | DOI
[6] On the tropical Torelli Map, Adv. Math., Volume 226 (2011) no. 3, pp. 2546-2586 | DOI
[7] Algebraic and tropical curves: comparing their moduli spaces, Handbook of Moduli, Volume I (Advanced Lectures in Mathematics), Volume 24, International Press, 2012, pp. 119-160
[8] Geometry of tropical moduli spaces and linkage of graphs, J. Comb. Theory, Ser., Volume 119 (2012) no. 3, pp. 579-598 | DOI
[9] Torelli theorem for graphs and tropical curves, Duke Math. J., Volume 153 (2010), pp. 129-171 | DOI
[10] Moduli spaces of rational weighed stable curves and tropical geometry (2016) (https://arxiv.org/abs/1404.7426, to appear in Forum of Mathematics)
[11] Tropicalizing the space of admissible covers, Math. Ann., Volume 364 (2016) no. 3-4, pp. 1275-1313 | DOI
[12] A tropical proof of the Brill–Noether Theorem, Adv. Math., Volume 230 (2012) no. 2, pp. 759-776 | DOI
[13] Introduction to algorithms, MIT Press, 2009, xix+1292 pages
[14] Toric varieties, Graduate Studies in Mathematics, 124, American Mathematical Society, 2011, xxiv+841 pages
[15] Limit linear series: Basic theory, Invent. Math., Volume 85 (1986), pp. 337-371 | DOI
[16] Linear systems and ramification points on reducible nodal curves, Mat. Contemp., Volume 14 (1998), pp. 21-35
[17] Limit canonical systems on curves with two components, Invent. Math., Volume 149 (2002) no. 2, pp. 267-338 | DOI
[18] Moduli spaces of weighted pointed stable curves, Adv. Math., Volume 173 (2003) no. 2, pp. 316-352 | DOI
[19] Veronese curves and Grothendieck-Knudsen moduli space , J. Algebr. Geom., Volume 2 (1993) no. 2, pp. 239-262
[20] Images of Rational Maps of Projective Spaces (2014) (https://arxiv.org/abs/1310.8453)
[21] Moduli space of enriched stable curves, Harvard University (UK) (1998) (Ph. D. Thesis)
[22] Moduli spaces of rational tropical curves, Proceedings of Gökova Geometry-Topology Conference 2006 (2007), pp. 39-51
[23] Tropical curves, their Jacobians and Theta functions, Proceedings of the International Conference on Curves and Abelian Varieties in Honor of Roy Smith’s 65th Birthday (Contemporary Mathematics), Volume 465 (2007), pp. 203-231
[24] A limit linear series moduli scheme, Ann. Inst. Fourier, Volume 56 (2006) no. 6, pp. 1165-1205 | DOI
[25] Limit linear series for curves not of compact type (2014) (https://arxiv.org/abs/1406.6699)
[26] Level- and stable limit linear series on singular curves, Instituto Nacional de Matemática Pura e Aplicada (Brazil) (2013) (Ph. D. Thesis)
[27] Tropical geometry of moduli spaces of weighted stable curves, J. Lond. Math. Soc., Volume 92 (2015) no. 2, pp. 427-450 | DOI
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