Uniform families of minimal rational curves on Fano manifolds

Abstract

It is a well-known fact that families of minimal rational curves on rational homogeneous manifolds of Picard number one are uniform, in the sense that the tangent bundle to the manifold has the same splitting type on each curve of the family. In this note we prove that certain --stronger-- uniformity conditions on a family of minimal rational curves on a Fano manifold of Picard number one allow to prove that the manifold is homogeneous.

References in corpus (3)

• A survey on the Campana-Peternell Conjecture
• Fano manifolds whose elementary contractions are smooth ${\mathbb{P}}^1$-fibrations: A geometric characterization of flag varieties
• Birationality of the tangent map for minimal rational curves

Cited by in corpus (1)

• A survey on the Campana-Peternell Conjecture