Nagoya Mathematical Journal

Simple normal crossing Fano varieties and log Fano manifolds

Kento Fujita

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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 rn/2 with ρ(X)2 or rn2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

Article information

Nagoya Math. J., Volume 214 (2014), 95-123.

First available in Project Euclid: 24 February 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J45: Fano varieties
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)


Fujita, Kento. Simple normal crossing Fano varieties and log Fano manifolds. Nagoya Math. J. 214 (2014), 95--123. doi:10.1215/00277630-2430136.

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