  A consistent N=1 supersymmetric $\sigma$-model can be constructed, given a
K\"ahler manifold by adding chiral matter multiplets. Their scalar components
are covariant tensors on the underlying K\"ahler manifold. The K\"ahler
U(1)-charges can be adjusted such that the anomalies cancel, using the
holomorphic functions in which the K\"ahler potential transforms. The
arbitrariness of the U(1)-charges of matter multiplets is related to their
Weyl-weights in superconformal gravity, before it is reduced to supergravity.
The covariance of the K\"ahler potential forces the superpotential to be
covariant as well. This relates the cut-off, the Planck scale and the matter
charges to each other. A non-vanishing VEV of the covariant superpotential
breaks the K\"ahler U(1) spontaneously. If this VEV vanishes, the gravitino is
massless and depending on the above mentioned parameters there may be
additional internal symmetry breaking. The separation of the different
representations of chiral multiplets can be achieved by covariantizations of
derivatives and fermions. Using non-holomorphic transformations, the full
K\"ahler metric can be block-diagonalized and the necessary covariantizations
come out naturally. Various aspects are illustrated by applying them to
Grassmannian coset models. In particular a consistent model of coset
$SU(5)/SU(2)\times U(1) \times SU(3)$ with the field content of the standard
model is constructed. The phenomenology of this model is analyzed.
