Spin canonical rings of log stacky curves
Annales de l'Institut Fourier, Volume 66 (2016) no. 6, p. 2339-2383

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.

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.

Received : 2015-07-16
Revised : 2016-01-30
Accepted : 2016-02-18
Published online : 2016-10-04
DOI : https://doi.org/10.5802/aif.3065
Classification:  14Q05,  11F11
Keywords: Modular forms, canonical rings, theta characteristic, Petri’s theorem, stacks, Groebner basis
@article{AIF_2016__66_6_2339_0,
     author = {Landesman, Aaron and Ruhm, Peter and Zhang, Robin},
     title = {Spin canonical rings of log stacky curves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {6},
     year = {2016},
     pages = {2339-2383},
     doi = {10.5802/aif.3065},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2016__66_6_2339_0}
}
Landesman, Aaron; Ruhm, Peter; Zhang, Robin. Spin canonical rings of log stacky curves. Annales de l'Institut Fourier, Volume 66 (2016) no. 6, pp. 2339-2383. doi : 10.5802/aif.3065. http://www.numdam.org/item/AIF_2016__66_6_2339_0/

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