Higher order minimal families of rational curves and Fano manifolds with   nef Chern characters
  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. 
Taku Suzuki
math.AG