We study smooth quadric surfaces in the Pfaffian hypersurface in parameterizing 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 .

中文翻译：

---

f14中Pfaffian超曲面的二次曲面

我们研究了Pfaffian超曲面中的光滑二次曲面 参数化 秩不超过4的不对称矩阵，不与其奇异位点相交。这样的表面对应于大小为6，阶数为4的歪斜对称矩阵的二次系统，并在二次曲面上产生全局生成的向量束E。我们分析了这些束及其几何形状，并将它们与。