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.

Hilbert squares of degeneracy loci / Fatighenti, E; Meazzini, F; Mongardi, G; Ricolfi, AT. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 1973-4409. - ELETTRONICO. - Early Access:(2022), pp. 1-31. [10.1007/s12215-022-00832-w]

Hilbert squares of degeneracy loci

Fatighenti, E
;
Meazzini, F;Mongardi, G;Ricolfi, AT
2022

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 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.
2022
Hilbert squares of degeneracy loci / Fatighenti, E; Meazzini, F; Mongardi, G; Ricolfi, AT. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 1973-4409. - ELETTRONICO. - Early Access:(2022), pp. 1-31. [10.1007/s12215-022-00832-w]
Fatighenti, E; Meazzini, F; Mongardi, G; Ricolfi, AT
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/916891
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