  The M-theory origin of the IIB gauged supergravities in nine dimensions,
classified according to the inequivalent classes of monodromy, is shown to
exactly corresponds to the global description of the supermembrane with central
charges. The global description is a realization of the sculpting mechanism of
gauging (arXiv:1107.3255) and it is associated to particular deformation of
fibrations. The supermembrane with central charges may be formulated in terms
of sections on symplectic torus bundles with SL(2,Z) monodromy. This global
formulation corresponds to the gauging of the abelian subgroups of SL(2,Z)
associated to monodromies acting on the target torus. We show the existence of
the trombone symmetry in the supermembrane formulated as a non-linear
realization of the SL(2,Z) symmetry and construct its gauging in terms of the
supermembrane formulated on an inequivalent class of symplectic torus
fibration. The supermembrane also exhibits invariance under T-duality and we
find the explicit T-duality transformation. It has a natural interpretation in
terms of the cohomology of the base manifold and the homology of the target
torus. We conjecture that this construction also holds for the IIA origin of
gauged supergravities in 9D such that the supermembrane becomes the origin of
all type II supergravities in 9D. The geometric structure of the symplectic
torus bundle goes beyond the classification on conjugated classes of SL(2,Z).
It depends on the elements of the coinvariant group associated to the monodromy
group. The possible values of the (p,q) charges on a given symplectic torus
bundle are restricted to the corresponding equivalence class defining the
element of the coinvariant group.
