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arXiv · 2204.00437

Hilbert squares of degeneracy loci

Enrico Fatighenti·Francesco Meazzini·Giovanni Mongardi·Andrea T. Ricolfi
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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.

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Enrico Fatighenti, Francesco Meazzini, Giovanni Mongardi, Andrea T. Ricolfi. 2022-04-01. Hilbert squares of degeneracy loci. https://arxiv.org/abs/2204.00437

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