[Quantification du cône canonique d'une courbe algébrique]
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”.
Keywords: algebraic curves, canonical cones, formal pseudodifferential operators, Rankin-Cohen brackets, Poincaré uniformization
Mot clés : courbes algébriques, cônes canoniques, opérateurs pseudodifférentiels formels, de Rankin-Cohen, uniformisation de Poincaré
@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},
pages = {1629--1663},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {52},
number = {6},
year = {2002},
doi = {10.5802/aif.1929},
mrnumber = {1952526},
zbl = {1052.14035},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1929/}
}
TY - JOUR AU - Enriquez, Benjamin AU - Odesskii, Alexander TI - Quantization of canonical cones of algebraic curves JO - Annales de l'Institut Fourier PY - 2002 SP - 1629 EP - 1663 VL - 52 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1929/ DO - 10.5802/aif.1929 LA - en ID - AIF_2002__52_6_1629_0 ER -
%0 Journal Article %A Enriquez, Benjamin %A Odesskii, Alexander %T Quantization of canonical cones of algebraic curves %J Annales de l'Institut Fourier %D 2002 %P 1629-1663 %V 52 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1929/ %R 10.5802/aif.1929 %G en %F 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) no. 6, pp. 1629-1663. doi : 10.5802/aif.1929. http://www.numdam.org/articles/10.5802/aif.1929/
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