论文标题
低等级的正交束和二次振动
Low rank orthogonal bundles and quadric fibrations
论文作者
论文摘要
令$ c $为曲线，$ v \ to c $ a级$ r $的正交矢量捆绑包。对于$ r \ le 6 $，可以使用张量，对称和较低等级捆绑的产品来描述$ v $的结构，这基本上是由于这些$ r $的$ \ mathrm {spin}（r，\ mathbb {c}）$之间存在异常的同构函数。我们详细分析了这些结构，特别是使用它们来描述正交束的模量空间。此外，$ V $中各向同性矢量的轨迹定义了四边形子纤维$ q_v \ subset \ mathbb {p} v $。利用低维四边形的熟悉结果，我们在$ V $的各向同性引号方案与某些普通引号方案之间表现出同构。特别是，对于$ r \ le 6 $，这提供了一种列举一般$ v $的最大程度的各向同性分组的方法，当时有很多。
Let $C$ be a curve and $V \to C$ an orthogonal vector bundle of rank $r$. For $r \le 6$, the structure of $V$ can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between $\mathrm{Spin} (r , \mathbb{C})$ and other groups for these $r$. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Furthermore, the locus of isotropic vectors in $V$ defines a quadric subfibration $Q_V \subset \mathbb{P} V$. Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of $V$ and certain ordinary Quot schemes of line subbundles. In particular, for $r \le 6$ this gives a method for enumerating the isotropic subbundles of maximal degree of a general $V$, when there are finitely many.
