Rational curves of minimal degree and characterizations of ${\mathbb P}^n$

Details Rational curves of minimal degree and characterizations of ${\mathbb P}^n$ Rational curves of minimal degree and characterizations of ${\mathbb P}^n$

2004-10-27

arxiv.org/abs/math/0410584v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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 $x\in X$ form a linear subspace of $T_xX$. As an application of our main result, we give a unified geometric proof of Mori's, Wahl's, Campana-Peternell's and Andreatta-Wi\'sniewski's characterizations of ${\mathbb P}^n$.

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