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 -(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 ρ(X)\geq 2 or r\geq n-2. This result is a partial generalization of the classification of logarithmic Fano threefolds by Maeda.

arXiv comment38 pages, minor revision; correct Theorem 2.7 and add references

References in corpus (5)

• On G-Fano threefolds
• Introduction to the log minimal model program for log canonical pairs
• Quasi-log varieties
• New examples of terminal and log canonical singularities
• Quotients by finite equivalence relations

Cited by in corpus (5)

• Asymptotically log Fano varieties
• On the structure of a log smooth pair in the equality case of the Bogomolov-Gieseker inequality
• The Mukai conjecture for log Fano manifolds
• Maximal log Fano manifolds are generalized Bott towers
• $d$-semistable Calabi--Yau threefolds of Type III