Quantization of canonical cones of algebraic curves
Abstract
We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve C, based on the theory of formal pseudodifferential operators. When C is a complex curve with Poincaré uniformization, we propose another, equivalent construction, based on the work of CohenManinZagier on RankinCohen brackets. We give a presentation of the quantum algebra when C is a rational curve, and discuss the problem of constructing algebraically "differential liftings".
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:math/0112148
 Bibcode:
 2001math.....12148E
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra
 EPrint:
 Ann. Inst. Fourier (Grenoble) 52 (2002), no. 6, 16291663