[Anneaux log-canoniques à spin des courbes champêtres]
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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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
@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},
pages = {2339--2383},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {6},
year = {2016},
doi = {10.5802/aif.3065},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3065/}
}
TY - JOUR AU - Landesman, Aaron AU - Ruhm, Peter AU - Zhang, Robin TI - Spin canonical rings of log stacky curves JO - Annales de l'Institut Fourier PY - 2016 SP - 2339 EP - 2383 VL - 66 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3065/ DO - 10.5802/aif.3065 LA - en ID - AIF_2016__66_6_2339_0 ER -
%0 Journal Article %A Landesman, Aaron %A Ruhm, Peter %A Zhang, Robin %T Spin canonical rings of log stacky curves %J Annales de l'Institut Fourier %D 2016 %P 2339-2383 %V 66 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3065/ %R 10.5802/aif.3065 %G en %F AIF_2016__66_6_2339_0
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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