  In this paper we prove the compactness result for compact K\"ahler Ricci
gradient shrinking solitons. If $(M_i,g_i)$ is a sequence of K\"ahler Ricci
solitons of real dimension $n \ge 4$, whose curvatures have uniformly bounded
$L^{n/2}$ norms, whose Ricci curvatures are uniformly bounded from below and
$\mu(g_i,1/2) \ge A$ (where $\mu$ is Perelman's functional), there is a
subsequence $(M_i,g_i)$ converging to a compact orbifold
$(M_{\infty},g_{\infty})$ with finitely many isolated singularitites, where
$g_{\infty}$ is a K\"ahler Ricci soliton metric in an orbifold sense (satisfies
a soliton equation away from singular points and smoothly extends in some gauge
to a metric satisfying K\"ahler Ricci soliton equation in a lifting around
singular points).
