  Generalization of the cross ratio to polarizations of linear finite and
infinite-dimensional spaces (in particular to Sato Grassmannian) is given and
explored. This cross ratio appears to be a cocycle of the canonical
(tautalogical) bundle over the Grassmannian with coefficients in the sheaf of
its endomorphisms. Operator analog of the Schwarz differential is defined. Its
connections to linear Hamiltonian systems and Riccati equations are
established. These constructions aim to obtain applications to KP-hierarchy.
