2010/03/25 by Gianluca Occhetta, Occhetta, Gianluca, Valentina Paterno +1
Mathematics · #14E30. #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary 14M22 #Secondary 14J40 #math.AG #msc:14E30. #msc:14J40 #msc:14M22
paper · pdf · doi:10.48550/arxiv.1003.4936
arxiv created 2010/03/25 · openalex publication_date 2010/03/25 · arxiv updated 2010/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study smooth complex projective polarized varieties (X,H) of dimension n ≥ 2 which admit a dominating family V of rational curves of H-degree 3, such that two general points of X may be joined by a curve parametrized by V, and such that there is a covering family of rational curves of H-degree one. Our main result is that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjuction theoretic scroll structure over a smooth variety.