A compactness result for Kahler Ricci solitons

In this paper we prove a compactness result for compact Kahler Ricci gradient shrinking solitons. If (M-i, g(i)) is a sequence of Kahler Ricci solitons of real dimension n >= 4, whose curvatures have uniformly bounded L-n/2 norms, whose Ricci curvatures are uniformly bounded from below and mu(g(i), 1/2)>=, A (where mu is Perelman's functional), there is a subsequence (M-i, g(i)) converging to a compact orbifold (M infinity, g infinity) with finitely many isolated singularities, where g infinity is a Kahler 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 Kahler Ricci soliton equation in a lifting around singular points). Published by Elsevier Inc.