论文标题
$ \ mathbb {p}^{14} $中的pfaffian hypersurface中的二次表面
Quadric surfaces in the Pfaffian hypersurface in $\mathbb{P}^{14}$
论文作者
论文摘要
我们在$ \ mathbb {p}^{14} $参数化$ 6 \ times 6 $ skew-Amperimempric-Metige-Metige-Metige-Metige-Metige-Metige-Metigy-Aftrices等级的$ \ Mathbb {p}^{14}中研究平滑的二次表面。这样的表面对应于6号和恒定等级4的偏度对称矩阵的二次系统，并引起了四边形上全球生成的矢量束$ e $。我们分析了这些捆绑包及其几何形状，将它们与$ \ Mathbb {p}^5 $中的线性一致性有关。
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 $\mathbb{P}^5$.
