  We summarize the global geometric formulation of Einstein-Scalar-Maxwell
theories twisted by flat symplectic vector bundle which encodes the duality
structure of the theory. We describe the scalar-electromagnetic symmetry group
of such models, which consists of flat unbased symplectic automorphisms of the
flat symplectic vector bundle lifting those isometries of the scalar manifold
which preserve the scalar potential. The Dirac quantization condition for such
models involves a local system of integral symplectic spaces, giving rise to a
bundle of polarized Abelian varieties equipped with a symplectic flat
connection, which is defined over the scalar manifold of the theory.
Generalized Einstein-Scalar-Maxwell models arise as the bosonic sector of the
effective theory of string/M-theory compactifications to four-dimensions, and
they are characterized by having non-trivial solutions of "U-fold" type.
