On the EKL-degree of a Weyl cover

JOURNAL OF ALGEBRA

卷:565

Article

Knight, Joseph¹  Swaminathan, Ashvin A.²  Tseng, Dennis³ 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[3] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

关键词: Degree;    Grothendieck-Witt ring;    Flag variety;    Non-algebraically closed fields;    Weyl group;   

DOI  :  10.1016/j.jalgebra.2020.08.018

来源: Elsevier

【 摘 要 】

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 Al-enumerative geometry. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free