Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Higher order minimal families of rational curves and Fano manifolds with nef Chern characters
Taku Suzuki
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2021 年 73 巻 3 号 p. 949-964

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In this paper, we investigate higher order minimal families 𝐻𝑖 of rational curves associated to Fano manifolds 𝑋. We prove that 𝐻𝑖 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.

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