We discuss an "infinite dimensional algebraic geometric" aproach to the moduli space of Lagragian cycles. It is based on the following series of observations. Each real symplectic manifold $M$ equipped with pequantization data and $\text{\sl Mp}^{\mathb CC}$-sructure produces an infinite dimensional Kaehler manifold $\mathcal B$, of half weighted Bohr - Sommerfeld cycles of fixed volume. This manifold admits a canonical prequantization equipment. The Poisson algebra of smooth functions on the initial symplectic manifold $M$ is naturally represented (as a Poisson subalgebra) in the Poisson algebra of smooth functions on this infinite dimensional manifold $\mathcal B$. A complex polarization of $M$ gives a canonical holomorphic map from $\mathcal B$ to the projective space of quantum states. This map has surjective differentials.
