On covering and quasi-unsplit families of rational curves

2005/04/04 by L. Bonavero, Bonavero, L., C. Casagrande +3 · 2 citations
Computer Science · Engineering · Mathematics · #14E30 #14J99 #14M99 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E30 #msc:14J99 #msc:14M99

paper · pdf · doi:10.48550/arxiv.math/0504056

13 pages

arxiv created 2005/04/04 · openalex publication_date 2005/04/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study extremality properties of covering families of rational curves on projective varieties. Among others, we show that on a normal and Q-factorial projective variety of dimension at most 4, every covering and quasi-unsplit family of rational curves generates a geometric extremal ray of the Mori cone.

Cited by

• Rationally cubic connected manifolds II
• Projective Q-factorial toric varieties covered by lines

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