  Kahler quantization of H1(T2,R) is studied. It is shown that this theory
corresponds to a fermionic sigma-model targeting a noncommutative space. By
solving the complex-structure moduli independence conditions, the quantum
background independent wave function is obtained. We study the transformation
of the wave function under modular transformation. It is shown that the
transformation rule is characteristic to the operator ordering. Similar results
are obtained for Kahler quantization of H2(T,R).
