Rational curves of minimal degree and characterizations of projective spaces |
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Authors: | Carolina Araujo |
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Institution: | (1) IMPA — Estrada Dona Castorina, 110, Rio de Janeiro, RJ, 22460-320, Brazil |
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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 . 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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Keywords: | |
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