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.
Fatighenti, E., Meazzini, F., Mongardi, G., Ricolfi, A.T. (2023). Hilbert squares of degeneracy loci. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 72(6), 3153-3183 [10.1007/s12215-022-00832-w].
Hilbert squares of degeneracy loci
Fatighenti, E
;Meazzini, F;Mongardi, G;Ricolfi, AT
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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