Correspondence between Projective bundles over ℙ² and rational Hypersurfaces in ℙ⁴

2023/12/14 by Shivam Vats, Vats, Shivam
Mathematics · #14M20(Secondary) #4E08 #4F17(Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2312.09096

openalex publication_date 2023/12/14 · openalex created_date 2023/12/16 · openalex updated_date 2026/07/28

Abstract

Let E be the restriction of the null-correlation bundle on ℙ³ to a hyperplane. In this article, we show that the projective bundle ℙ(E) is isomorphic to a blow-up of a non-singular quadric in ℙ⁴ along a line. We also prove that for each d ≥ 2, there are hypersurfaces of degree d containing a line in ℙ⁴ whose blow-up along the line is isomorphic to the projective bundle over ℙ².

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