  Greene, Morrison and Plesser \cite{GMP} have recently suggested a general
method for constructing a mirror map between a $d$-dimensional Calabi-Yau
hypersurface and its mirror partner for $d > 3$. We apply their method to
smooth hypersurfaces in weighted projective spaces and compute the Chern
numbers of holomorphic curves on these hypersurfaces. As anticipated, the
results satisfy nontrivial integrality constraints. These examples differ from
those studied previously in that standard methods of algebraic geometry which
work in the ordinary projective space case for low degree curves are not
generally applicable. In the limited special cases in which they do work we can
get independent predictions, and we find agreement with our results.
