  We study the type II superstring theory on the background $\br^{d-1,1}\times
X_n$, where $X_n$ is a Calabi-Yau $n$-fold ($2n+d=10$) with an isolated
singularity, by making use of the holographically dual description proposed by
Giveon-Kutasov-Pelc (hep-th/9907178). We compute the toroidal partition
functions for each of the cases $d=6,4,2$, and obtain manifestly modular
invariant solutions classified by the standard $A-D-E$ series corresponding to
the type of singularities on $X_n$. Partition functions of these modular
invariants all vanish due to theta function identities and are consistent with
the presence of space-time supersymmetry.
