Lengths of chains of minimal rational curves on Fano manifolds

Kiwamu Watanabe

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arXiv · 1010.2002

Lengths of chains of minimal rational curves on Fano manifolds

Kiwamu Watanabe

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Abstract

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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BibTeX RIS

Kiwamu Watanabe. 2010-10-11. Lengths of chains of minimal rational curves on Fano manifolds. https://arxiv.org/abs/1010.2002

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