On the minimal length of extremal rays for Fano 4-folds

Details On the minimal length of extremal rays for Fano 4-folds On the minimal length of extremal rays for Fano 4-folds

2010-05-11

arxiv.org/abs/1005.1722v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

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.

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