Theta-functions on T^2-bundles over T^2 with the Euler class zero

Abstract

We construct an analogue of the classical theta-function on an Abelian variety for closed 4-dimensional symplectic manifolds which are T^2-bundles over T^2 with the zero Euler class. We use our theta-functions for a canonical symplectic embedding of these manifolds into complex projective spaces (an analogue of the Lefschetz theorem).