Quantization of canonical cones of algebraic curves

Details Quantization of canonical cones of algebraic curves Quantization of canonical cones of algebraic curves

2001-12-14

arxiv.org/abs/math/0112148v2

Ann. Inst. Fourier (Grenoble) 52 (2002), no. 6, 1629-1663

Mathematics

Algebraic Geometry

Scientific paper

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 Poincar\'e 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 C is a rational curve, and discuss the problem of constructing algebraically "differential liftings".

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