Chains of minimal rational curves

Jun-Muk Hwang

KIAS, Korea

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Abstract

Chains of minimal rational curves have been used as an important tool in the study of Fano manifolds. In a joint work with S. Kebekus, we introduce an infinitesimal method to study chains of minimal rational curves via varieties of minimal rational tangents and their higher secants. For many examples of Fano manifolds, this method can be used to compute the minimal length of chains needed to join two general points.