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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73026In 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-Wiśniewski's characterizations of ${\mathbb P}^n$.14 pagesAlgebraic Geometry14E08; 14J40Rational curves of minimal degree and characterizations of ${\mathbb P}^n$text