Hilbert squares of degeneracy loci

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 Hilb 2 ( S ) is isomorphic to the zero locus of a global section of an irreducible homogeneous vector...

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Bibliographic Details
Published inRendiconti del Circolo matematico di Palermo Vol. 72; no. 6; pp. 3153 - 3183
Main Authors Fatighenti, Enrico, Meazzini, Francesco, Mongardi, Giovanni, Ricolfi, Andrea T.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2023
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Isomorphism
Mathematical analysis
Mathematics
Mathematics and Statistics
Grassmannians
Degeneracy loci
Hilbert schemes
Fano varieties
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Summary: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 Hilb 2 ( 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.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-022-00832-w