  After reviewing the existing results we give an extensive analysis of the
critical points of the potentials of the gauged N=2 Yang-Mills/Einstein
Supergravity theories coupled to tensor- and hyper multiplets. Our analysis
includes all the possible gaugings of all N=2 Maxwell-Einstein supergravity
theories whose scalar manifolds are symmetric spaces. In general, the scalar
potential gets contributions from R-symmetry gauging, tensor couplings and
hyper-couplings. We show that the coupling of a hypermultiplet into a theory
whose potential has a non-zero value at its critical point, and gauging a
compact subgroup of the hyperscalar isometry group will only rescale the value
of the potential at the critical point by a positive factor, and therefore will
not change the nature of an existing critical point. However this is not the
case for non-compact SO(1,1) gaugings. An SO(1,1) gauging of the hyper isometry
will generally lead to deSitter vacua, which is analogous to the ground states
found by simultaneously gauging SO(1,1) symmetry of the real scalar manifold
with U(1)_R in earlier literature. SO(m,1) gaugings with m>1, which give
contributions to the scalar potential only in the Magical Jordan family
theories, on the other hand, do not lead to deSitter vacua. Anti-deSitter vacua
are generically obtained when the U(1)_R symmetry is gauged. We also show that
it is possible to embed certain generic Jordan family theories into the Magical
Jordan family preserving the nature of the ground states. However the Magical
Jordan family theories have additional ground states which are not found in the
generic Jordan family theories.
