Quantization of of an elliptic curve can be done in different ways.
one can start with the
C^*-algebra of continuous functions on ordinary torus and by inserting a deformation parameter
\theta into the product obtain a deformed non-commutaive
C^*-algebra of functions on the quantum torus.
My question is:
Is there any natural way for deformation quantization of closed Riemann surfaces with higher genus in the above sense?