no. 6
Spin canonical rings of log stacky curves
[Anneaux log-canoniques à spin des courbes champêtres]
Landesman, Aaron1 ; Ruhm, Peter2 ; Zhang, Robin2
1 Department of Mathematics Harvard University One Oxford Street Cambridge MA 02138 (USA)
2 Department of Mathematics Stanford University Building 380 Stanford CA 94305 (USA)
Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2339-2383.

Considérons les formes modulaires d’un quotient d’aire finie du demi-plan de Poincaré par un groupe fuchsien. D’après un résultat classique de Kodaira–Spencer, cet anneau de formes modulaires peut être considéré comme l’anneau log-canonique à spin d’une courbe champêtre. Dans cet article, nous obtenons une borne optimale pour les degrés des générateurs minimaux et des relations minimales d’un tel anneau, et donc des anneaux de formes modulaires de poids entier arbitraire.

Consider modular forms arising from a finite-area quotient of the upper-half plane by a Fuchsian group. By the classical results of Kodaira–Spencer, this ring of modular forms may be viewed as the log spin canonical ring of a stacky curve. In this paper, we tightly bound the degrees of minimal generators and relations of log spin canonical rings. As a consequence, we obtain a tight bound on the degrees of minimal generators and relations for rings of modular forms of arbitrary integral weight.

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DOI : 10.5802/aif.3065
Classification : 14Q05, 11F11
Keywords: Modular forms, canonical rings, theta characteristic, Petri’s theorem, stacks, Groebner basis
Mot clés : Formes modulaires, anneaux canoniques, thêta-caractéristiques, théorème de Pétri, champs algébriques, base de Gröbner

Landesman, Aaron 1 ; Ruhm, Peter 2 ; Zhang, Robin 2

1 Department of Mathematics Harvard University One Oxford Street Cambridge MA 02138 (USA)
2 Department of Mathematics Stanford University Building 380 Stanford CA 94305 (USA) 
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Landesman, Aaron; Ruhm, Peter; Zhang, Robin. Spin canonical rings of log stacky curves. Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2339-2383. doi : 10.5802/aif.3065. https://aif.centre-mersenne.org/articles/10.5802/aif.3065/

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