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Quantization of canonical cones of algebraic curves

B. Enriquez·A. Odesskii
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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 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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B. Enriquez, A. Odesskii. 2001-12-14. Quantization of canonical cones of algebraic curves. https://arxiv.org/abs/math/0112148

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