QUANTUM RIEMANN SURFACES FOR ARBITRARY PLANCKS-CONSTANT

We continue our study of quantum Riemann surfaces initiated in Refs. 1 -3 [S. Klimek and A. Lesniewski, Commun. Math. Phys. 146, 103-122 (199 2); Lett. Math. Phys. 24, 125-139 (1992); 32, 45-61 (1994)]. We constr uct a one parameter family of deformations of compact Riemann surfaces of genus g greater than or equal to 2. Our construction does not requ ire any discreteness condition on the value of Planck's constant. It c oincides with the construction of Ref. 2 [Lett. Math. Phys. 24, 125-13 9 (1992)] in the case when Planck's constant assumes the discrete set of values dictated by geometric quantization. (C) 1996 American Instit ute of Physics.