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

2010/10/11 by Kiwamu Watanabe, Watanabe, Kiwamu
Mathematics · #14E30 #14J45 #14N99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #msc:14E30 #msc:14J45 #msc:14N99

paper · pdf · doi:10.48550/arxiv.1010.2005

10 pages. Correct minor erros. Improved exposition

openalex publication_date 2010/10/11 · arxiv created 2011/04/25 · arxiv updated 2011/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Geometry of chains of minimal rational curves
• Rational curves and bounds on the Picard number of Fano manifolds
• Bounds on the Picard rank of toric Fano varieties with minimal curve constraints
• Fano manifolds obtained by blowing up along curves with maximal Picard number
• Locally unsplit families of rational curves of large anticanonical degree on Fano manifolds