SIMPLE NORMAL CROSSING FANO VARIETIES AND LOG FANO MANIFOLDS

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 -(K-X + 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 rho(X) >= 2 or r >= n - 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.