Quadric surfaces in the Pfaffian hypersurface in ℙ¹⁴

2020/08/10 by Ada Boralevi, Boralevi, Ada, Maria Lucia Fania +3
Mathematics · #14F05 #14M15 #14N05 #15A30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2008.04292

openalex publication_date 2020/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study smooth quadric surfaces in the Pfaffian hypersurface in ℙ¹⁴ parameterising 6 × 6 skew-symmetric matrices of rank at most 4, not intersecting the Grassmannian \mathbbG(1,5). Such surfaces correspond to quadratic systems of skew-symmetric matrices of size 6 and constant rank 4, and give rise to a globally generated vector bundle E on the quadric. We analyse these bundles and their geometry, relating them to linear congruences of lines in ℙ⁵.

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