Simple normal crossing Fano varieties and log Fano manifolds

Abstract

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 3-folds by Maeda.