  We give a precise estimate of the Bergman kernel for the model domain defined
by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where
$F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$,
in terms of the complex singularity exponent of $F$.

Complex Variables