Given a vector bundle on a ${\mathbb{P}}^1$ bundle, the base is stratified by degeneracy loci measuring the splitting type of the vector bundle restricted to each fiber. The classes of these degeneracy loci in the Chow ring or cohomology ring of the base are natural invariants characterizing the degenerations of the vector bundle. When these degeneracy loci occur in the expected codimension, we find their classes. This yields universal formulas for degeneracy classes in terms of naturally arising vector bundles on the base. The existence of these formulas is applied to prove the non-emptiness of Brill-Noether splitting loci in [21]. Our results hold over arbitrary fields of any characteristic.

给定一个向量束 ${\mathbb{P}}^{\mathrm{1个}}$通过将简并基因座测量限制在每根光纤上的矢量束的分裂类型来对碱基进行分层。碱基的Chow环或同调环中的这些简并基因座的类别是表征载体束简并性的天然不变量。当这些简并基因座出现在预期的维数中时，我们找到它们的类。这样就产生了基于自然产生的矢量束的简并类的通用公式。这些公式的存在可用于证明[21]中的Brill-Noether分裂基因座为非空。我们的结果涵盖了任何特征的任意字段。