Rationally cubic connected manifolds II

2010/09/20 by Gianluca Occhetta, Occhetta, Gianluca, Valentina Paterno +1
Mathematics · #14E30 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #Primary 14M22 #Secondary 14J40 #math.AG #msc:14E30 #msc:14J40 #msc:14J45 #msc:14M22

paper · pdf · doi:10.48550/arxiv.1009.3811

25 pages, 5 figures

arxiv created 2010/09/20 · openalex publication_date 2010/09/20 · arxiv updated 2010/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 which do not admit a covering family of lines (i.e. rational curves of H-degree one). We prove that such manifolds are obtained from RCC manifolds of Picard number one by blow-ups along smooth centers. If we further assume that X is a Fano manifold, we obtain a stronger result, classifying all Fano RCC manifolds of Picard number ρ_X ≥ 3

Citations

• On covering and quasi-unsplit families of rational curves

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