  We study perturbations around the generalized Kazakov multicritical
one-matrix model. The multicritical matrix model has a potential where the
coefficients of $z^n$ only fall off as a power $1/n^{s+1}$. This implies that
the potential and its derivatives have a cut along the real axis, leading to
technical problems when one performs perturbations away from the generalized
Kazakov model. Nevertheless it is possible to relate the perturbed partition
function to the tau-function of a KdV hierarchy and solve the model by a genus
expansion in the double scaling limit.
