A bound of lengths of chains of minimal rational curves on Fano manifolds of Picard number 1

Details A bound of lengths of chains of minimal rational curves on Fano manifolds of Picard number 1 A bound of lengths of chains of minimal rational curves on Fano manifolds of Picard number 1

2010-10-11

arxiv.org/abs/1010.2005v3

Mathematics

Algebraic Geometry

10 pages. Correct minor erros. Improved exposition

Scientific paper

In this paper, we investigate the minimal length of chains of minimal
rational curves needed to join two general points on a Fano manifold of Picard
number 1. In particular, we give a sharp bound of the length by a fundamental
argument. As an application, we compute the length for Fano manifolds of
dimension < 8.

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