Nous construisons des quantifications de l’algèbre de Poisson des fonctions sur le cône canonique d’une courbe algébrique , qui s’appuie sur la théorie des opérateurs pseudodifférentiels formels. Quand est une courbe complexe munie d’une uniformisation de Poincaré, nous proposons une construction équivalente, basée sur le travail de Cohen- Manin-Zagier sur les crochets de Rankin-Cohen. Quand est une courbe rationnelle, nous donnons une présentation de l’algèbre quantique, et nous discutons le problème de la construction algébrique de “relèvements différentiels”.
We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve , based on the theory of formal pseudodifferential operators. When is a complex curve with Poincaré uniformization, we propose another, equivalent construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a presentation of the quantum algebra when is a rational curve, and discuss the problem of constructing algebraically “differential liftings”.
@article{AIF_2002__52_6_1629_0,
author = {Enriquez, Benjamin and Odesskii, Alexander},
title = {Quantization of canonical cones of algebraic curves},
journal = {Annales de l'Institut Fourier},
volume = {52},
year = {2002},
pages = {1629-1663},
doi = {10.5802/aif.1929},
mrnumber = {1952526},
zbl = {1052.14035},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2002__52_6_1629_0}
}
Enriquez, Benjamin; Odesskii, Alexander. Quantization of canonical cones of algebraic curves. Annales de l'Institut Fourier, Tome 52 (2002) pp. 1629-1663. doi : 10.5802/aif.1929. http://gdmltest.u-ga.fr/item/AIF_2002__52_6_1629_0/
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