Higher order minimal families of rational curves and Fano manifolds with nef Chern characters

摘要

In this paper, we investigate higher order minimal families H_i of rational curves associated to Fano manifolds X. We prove that H_i is also a Fano manifold if the Chern characters of X satisfy some positivity conditions. We also provide a sufficient condition for Fano manifolds to be covered by higher rational manifolds.