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, Enrico; Meazzini, Francesco; Mongardi, Giovanni; Ricolfi, Andrea T.. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 72:6(2023), pp. 3153-3183. [10.1007/s12215-022-00832-w]
Hilbert squares of degeneracy loci
Fatighenti, Enrico
;Meazzini, Francesco
;Mongardi, Giovanni
;Ricolfi, Andrea T.
2023
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.| File | Dimensione | Formato | |
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