2010/05/11 by Toru Tsukioka, Tsukioka, Toru
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1005.1722
The minimum of intersection numbers of the anti-canonical divisor with rational curves on a Fano manifold is called pseudo-index. It is expected that the intersection number of anti-canonical divisor attains to the minimum on an extremal ray, i.e. there exists an extremal rational curve whose intersection number with the anti-canonical divisor equals the pseudo-index. In this note, we prove this for smooth Fano 4-folds having birational contractions.