We study smooth quadric surfaces in the Pfaffian hypersurface in P^{14} parameterizing 6x6 skew-symmetric matrices of rank at most 4, not intersecting its singular locus. Such surfaces correspond to quadratic systems of skew-symmetric matrices of size 6 and constant rank 4, and give rise to a globally generated vector bundle E on the quadric. We analyse these bundles and their geometry, relating them to linear congruences in P^5.
Quadric surfaces in the Pfaffian hypersurface in P^14 / Boralevi, Ada; Lucia Fania, Maria; Mezzetti, Emilia. - In: LINEAR & MULTILINEAR ALGEBRA. - ISSN 0308-1087. - ELETTRONICO. - (2022), pp. 1-20. [Epub ahead of print] [10.1080/03081087.2021.1895048]
Quadric surfaces in the Pfaffian hypersurface in P^14
Emilia Mezzetti
2022-01-01
Abstract
We study smooth quadric surfaces in the Pfaffian hypersurface in P^{14} parameterizing 6x6 skew-symmetric matrices of rank at most 4, not intersecting its singular locus. Such surfaces correspond to quadratic systems of skew-symmetric matrices of size 6 and constant rank 4, and give rise to a globally generated vector bundle E on the quadric. We analyse these bundles and their geometry, relating them to linear congruences in P^5.| File | Dimensione | Formato | |
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