  In the first part of this paper we find supergravity solutions corresponding
to branes on worldvolumes of the form $R^d \times \Sigma$ where $\Sigma$ is a
Riemann surface. These theories arise when we wrap branes on holomorphic
Riemann surfaces inside $K3$ or CY manifolds. In some cases the theory at low
energies is a conformal field theory with two less dimensions. We find some
non-singular supersymmetric compactifications of M-theory down to $AdS_5$. We
also propose a criterion for permissible singularities in supergravity
solutions.
  In the second part of this paper, which can be read independently of the
first, we show that there are no non-singular Randall-Sundrum or de-Sitter
compactifications for large class of gravity theories.
