Hilbert squares of degeneracy loci

2022/04/01 by Enrico Fatighenti, Fatighenti, Enrico, Francesco Meazzini +5
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2204.00437

openalex publication_date 2022/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in ℙ^s. We prove that, under certain positivity conditions, its Hilbert square Hilb²(S) is isomorphic to the zero locus of a global section of an irreducible homogeneous vector bundle on a product of Grassmannians. Our construction involves a naturally associated Fano variety, and an explicit description of the isomorphism.

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