1. On the EKL-Degree of a Weyl Cover
- Author
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Knight, Joseph, Swaminathan, Ashvin, and Tseng, Dennis
- Subjects
Mathematics - Algebraic Geometry ,Mathematics - Number Theory ,Mathematics - Representation Theory ,14M15, 55M25, 14F42, 14G27 - Abstract
More than four decades ago, Eisenbud, Khim\v{s}ia\v{s}vili, 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 $f\colon \mathbb{A}^n\to \mathbb{A}^n$ 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 $\mathbb{A}^1$-enumerative geometry., Comment: 15 pages
- Published
- 2019