## Nagoya Mathematical Journal

### Simple normal crossing Fano varieties and log Fano manifolds

Kento Fujita

#### 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 $-(K_{X}+D)$ 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 $r\geq n/2$ with $\rho(X)\geq2$ or $r\geq n-2$. This result is a partial generalization of the classification of logarithmic Fano $3$-folds by Maeda.

#### Article information

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

Dates
First available in Project Euclid: 24 February 2014

https://projecteuclid.org/euclid.nmj/1393251538

Digital Object Identifier
doi:10.1215/00277630-2430136

Mathematical Reviews number (MathSciNet)
MR3211820

Zentralblatt MATH identifier
1297.14047

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

#### Citation

Fujita, Kento. Simple normal crossing Fano varieties and log Fano manifolds. Nagoya Math. J. 214 (2014), 95--123. doi:10.1215/00277630-2430136. https://projecteuclid.org/euclid.nmj/1393251538

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