Geometric formulation of quantum mechanics, proposed by A. Ashtekar and T. Schilling, implies a generalization of the standard geometric quantization problem for compact symplectic manifolds.Instead of a Hilbert space one is looking for a Kahler manifold (finite or infinite dimensional). The moduli space of half weighted Bohr - Sommerfeld lagrangian submanifolds of fixed topological type and volume, introduced by Andrey Tyurin and Alexei Gorodentsev in 1999, can be exploited in this framework as a space of quantum states for a new quantization method in the framework of algebraic lagrangian geometry