We study smooth quadric surfaces in the Pfaan hypersurface in P^14 parameterising 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

Maria Lucia Fania;
2021

Abstract

We study smooth quadric surfaces in the Pfaan hypersurface in P^14 parameterising 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/161895
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