  The complex version of Bohr-Sommerfeld conditions is proposed. The
BPU-construction (see [D.Borthwick, T. Paul and A. Uribe, Legendrian
distributions with applications to the non-vanishing of Poincar\'e series of
large weight, Invent. math, 122 (1995), 359-402, preprint hep-th/9406036] or
[Andrei Tyurin, On Bohr-Sommerfeld bases, math.AG/9909084]) is generalized to
this complexification. The new feature of this generalization is a spectral
curve. The geometry of such curves is investigated.

Algebraic Geometry;Symplectic Geometry