A projective log variety is called a log Fano manifold if is smooth and if is a reduced simple normal crossing divisor on with ample. The -dimensional log Fano manifolds with nonzero are classified in this article when the log Fano index of satisfies either with or . This result is a partial generalization of the classification of logarithmic Fano -folds by Maeda.
"Simple normal crossing Fano varieties and log Fano manifolds." Nagoya Math. J. 214 95 - 123, June 2014. https://doi.org/10.1215/00277630-2430136