  We develop some ideas of Morrison and Plesser and formulate a precise
mathematical conjecture which has close relations to toric mirror symmetry. Our
conjecture, we call it Toric Residue Mirror Conjecture, claims that the
generating functions of intersection numbers of divisors on a special sequence
of simplicial toric varieties are power series expansions of some rational
functions obtained as toric residues. We expect that this conjecture holds true
for all Gorenstein toric Fano varieties associated with reflexive polytopes and
give some evidences for that. The proposed conjecture suggests a simple method
for computing Yukawa couplings for toric mirror Calabi-Yau hypersurfaces
without solving systems of differential equations. We make several explicit
computations for Calabi-Yau hypersurfaces in weighted projective spaces and in
products of projective spaces.
