Abstract
In this paper we investigate complex uniruled varieties X whose rational curves of minimal degree satisfy a special property. Namely, we assume that the tangent directions to such curves at a general point x ∈ X form a linear subspace of TxX. As a first application of our main result, we give a unified geometric proof of Mori's, Wahl's, Campana-Peternell's and Andreatta-Wiśniewski's characterizations of Open image in new window. We also give a characterization of products of projective spaces in terms of the geometry of their families of rational curves of minimal degree.
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