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.
The author is supported by Grant-in-Aid for Research Activity Start-up from the Japan Society for the Promotion of Science.
"Higher order minimal families of rational curves and Fano manifolds with nef Chern characters." J. Math. Soc. Japan 73 (3) 949 - 964, July, 2021. https://doi.org/10.2969/jmsj/84428442