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In this paper we prove a compactness result for compact Kähler Ricci gradient shrinking solitons. If (Mi,gi) is a sequence of Kähler Ricci solitons of real dimension n⩾4, whose curvatures have uniformly bounded Ln/2 norms, whose Ricci curvatures are uniformly bounded from below and μ(gi,1/2)⩾A (where μ is Perelman's functional), there is a subsequence (Mi,gi) converging to a compact orbifold (M∞,g∞)...
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