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Simple normal crossing Fano varieties and log Fano manifolds

Published online by Cambridge University Press:  11 January 2016

Kento Fujita
Kento Fujita*
Affiliation:
Research Institute for Mathematical Sciences Kyoto UniversityKyoto 606-8502Japanfujita@kurims.kyoto-u.ac.jp
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Abstract

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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 Χ with − (KΧ + 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.

Keywords

14J4514E30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 214 , June 2014 , pp. 95 - 123
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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