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

Ada Boralevi; Maria Lucia Fania; Emilia Mezzetti

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arXiv · 2008.04292

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

Ada Boralevi·Maria Lucia Fania·Emilia Mezzetti

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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 $\mathbb{P}^5$.

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BibTeX RIS

Ada Boralevi, Maria Lucia Fania, Emilia Mezzetti. 2020-08-10. Quadric surfaces in the Pfaffian hypersurface in $\mathbb{P}^{14}$. https://arxiv.org/abs/2008.04292

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