Lengths of chains of minimal rational curves on Fano manifolds

Details Lengths of chains of minimal rational curves on Fano manifolds Lengths of chains of minimal rational curves on Fano manifolds

2010-10-11

arxiv.org/abs/1010.2002v1

Journal of Algebra Volume 325, Issue 1, 1 January 2011, Pages 163-176

Mathematics

Algebraic Geometry

16 pages. To appear in Journal of Algebra

Scientific paper

In this paper, we consider a natural question how many minimal rational curves are needed to join two general points on a Fano manifold X of Picard number 1. In particular, we study the minimal length of such chains in the cases where the dimension of X is at most 5, the coindex of X is at most 3 and X equips with a structure of a double cover. As an application, we give a better bound on the degree of Fano 5-folds of Picard number 1.

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