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

Abstract

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.

arXiv comment14 pages

Cited by in corpus (2)

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• On a sufficient condition for a Fano manifold to be covered by rational $N$-folds