Mirror Symmetry for Two Parameter Models -- II

We describe in detail the space of the two K\"ahler parameters of the
Calabi--Yau manifold $\P_4^{(1,1,1,6,9)}[18]$ by exploiting mirror symmetry.
The large complex structure limit of the mirror, which corresponds to the
classical large radius limit, is found by studying the monodromy of the periods
about the discriminant locus, the boundary of the moduli space corresponding to
singular Calabi--Yau manifolds. A symplectic basis of periods is found and the
action of the $Sp(6,\Z)$ generators of the modular group is determined. From
the mirror map we compute the instanton expansion of the Yukawa couplings and
the generalized $N=2$ index, arriving at the numbers of instantons of genus
zero and genus one of each degree. We also investigate an $SL(2,\Z)$ symmetry
that acts on a boundary of the moduli space.