Abstract More than four decades ago, Eisenbud, Khimsiasvili, and Levine introduced an analogue in the algebro-geometric setting of the notion of local degree from differential topology. Their notion of degree, which we call the EKL-degree, can be thought of as a refinement of the usual notion of local degree in algebraic geometry that works over non-algebraically closed base fields, taking values in the Grothendieck-Witt ring. In this note, we compute the EKL-degree at the origin of certain finite covers f : A n → A n induced by quotients under actions of Weyl groups. We use knowledge of the cohomology ring of partial flag varieties as a key input in our proofs, and our computations give interesting explicit examples in the field of A 1 -enumerative geometry.

中文翻译：

---

关于 Weyl 覆盖的 EKL 度

摘要 四十多年前，Eisenbud、Khimsiasvili 和 Levine 从微分拓扑中引入了局部度概念的代数几何设置中的类似物。他们的度数概念，我们称之为 EKL 度数，可以被认为是代数几何中通常的局部度数概念的改进，该概念适用于非代数封闭的基域，取 Grothendieck-Witt 环中的值。在本笔记中，我们计算某些有限覆盖 f 的原点的 EKL 度：A n → A n 由外尔群作用下的商引起。我们使用部分标志变体的上同调环的知识作为我们证明的关键输入，我们的计算在 A 1 枚举几何领域给出了有趣的明确例子。