Rational curves of minimal degree and characterizations of \mathbb Pⁿ

2004/10/27 by Carolina Araujo, Araujo, Carolina
Computer Science · Mathematics · #14E08 #14J40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #math.AG #msc:14E08 #msc:14J40

paper · pdf · doi:10.48550/arxiv.math/0410584

14 pages

arxiv created 2004/10/27 · openalex publication_date 2004/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 Pⁿ.

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