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Hilbert squares of degeneracy loci (2204.00437v1)
Published 1 Apr 2022 in math.AG
Abstract: Let $S$ be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in $\mathbb{P}s$. We prove that, under certain positivity conditions, its Hilbert square $\mathrm{Hilb}2(S)$ 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.