  Compactifications of M-theory on singular manifolds contain additional
charged massless states descending from M-branes wrapped on vanishing cycles.
We construct the first explicit example of a complete supergravity Lagrangian
that includes such extra states. This is done for a compactification on a
Calabi-Yau threefold that develops a genus zero curve of A_1 singularities at
the boundary of the K\"ahler cone with a resulting SU(2) gauge symmetry
enhancement. The corresponding SU(2) gauged supergravity Lagrangian includes
two charged and two neutral vector multiplets, and turns out to be uniquely
fixed by the Calabi-Yau geometry and by the effective ungauged Lagrangian
describing the Coulomb branch. One can see explicitly how resolving the
singularity corresponds to a supersymmetric Higgs effect in the gauged
supergravity description. The elementary transformation relating the two
families of smooth Calabi-Yau resolutions of the singularity acts as the SU(2)
Weyl twist. The resulting structure appears to be very rigid and is likely to
apply to other types of singularities and manifolds as well.
