COMPUTATION OF YUKAWA COUPLINGS FOR CALABI-YAU HYPERSURFACES IN WEIGHTED PROJECTIVE SPACES

B.R. Greene, D.R. Morrison and M.R. Plesser [Mirror Manifolds in Highe r Dimension, CLNS-93/1253, IASSNS-HEP-94-2, YCTP-92] have recently sug gested a general method for constructing a mirror map between a d-dime nsional Calabi-Yau hypersurface and its mirror partner for d > 3. We a pply their method to smooth hypersurfaces in weighted projective space s and compute the Chern numbers of holomorphic curves on these hypersu rfaces. As anticipated, the results satisfy nontrivial integrality con straints. These examples differ from those studied previously in that standard methods of algebraic geometry which work in the ordinary proj ective space case for low degree curves are not generally applicable. In the limited special cases in which they do work we can get independ ent predictions, and we find agreement with our results.