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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”.
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