Hilbert squares of degeneracy loci
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...
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Published in | Rendiconti del Circolo matematico di Palermo Vol. 72; no. 6; pp. 3153 - 3183 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.10.2023
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0009-725X 1973-4409 |
DOI: | 10.1007/s12215-022-00832-w |