Quadric surfaces in the Pfaffian hypersurface in ${\mathbb{P}}^{14}$

Abstract

We study smooth quadric surfaces in the Pfaffian hypersurface in ${\mathbb{P}}^{14}$ parameterising $6\times 6$ skew-symmetric matrices of rank at most 4, not intersecting the Grassmannian $\mathbb{G}(1,5)$. 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 of lines in ${\mathbb{P}}^5$.

18 pages

References in corpus (1)

• Pfaffian representations of cubic threefolds