  We give a characterizaton of smooth ample Hypersurfaces in Abelian Varieties
and also describe an irreducible connected component of their moduli space: it
consists of the Hypersurfaces of a given polarization type, plus the iterated
univariate coverings of normal type (of the same polarization type).
  The above manifolds yield also a connected component of the open set of
Teichm\"uller space consisting of K\"ahler complex structures.
