Hilbert squares of degeneracy loci
| Autor: | Fatighenti, Enrico, Meazzini, Francesco, Mongardi, Giovanni, Ricolfi, Andrea T. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 20 pages, comments welcome! |
| Databáze: | arXiv |
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