Weak Fano threefolds arising as the blowup of a hyperquadric in ℙ⁴ along a curve

2025/12/23 by Anne Schnattinger, Schnattinger, Anne
Mathematics · #14E05 #14E30 #14H99 #14J28 #14J30 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2512.20315

openalex publication_date 2025/12/23 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28

Abstract

We characterize smooth irreducible curves C on a smooth hyperquadric Y of ℙ⁴ such that the blowup of Y along C is a weak Fano threefold. These are precisely the smooth irreducible curves C of degree d and genus g lying on a smooth hypercubic section of Y such that (i) C has no 4-secant line and no 7-secant conic; (ii) d< 18 and (g,d)\not ∈ \(4,7), (10, 11)\; (iii) either 3d-26

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