Simple normal crossing Fano varieties and log Fano manifolds

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A projective log variety (X, D) is called "a log Fano manifold" if X is smooth and if D is a reduced simple normal crossing divisor on X with -(Kₓ+D) ample. The n-dimensional log Fano manifolds (X, D) with nonzero D are classified in this article when the log Fano index r of (X, D) satisfies either r≥ n/2 with ρ(X)≥ 2 or r≥ n-2. This result is a partial generalization of the classification of logarithmic Fano threefolds by Maeda.