The class of Eisenbud-Khimshiashvili-Levine is the local A 1 -Brouwer degree

Journal Article (Journal Article)

Given a polynomial function with an isolated zero at the origin, we prove that the local A1-Brouwer degree equals the Eisenbud-Khimshiashvili-Levine class. This answers a question posed by David Eisenbud in 1978. We give an application to counting nodes, together with associated arithmetic information, by enriching Milnor's equality between the local degree of the gradient and the number of nodes into which a hypersurface singularity bifurcates to an equality in the Grothendieck-Witt group.

Full Text

Duke Authors

Cited Authors

  • Kass, JL; Wickelgren, K

Published Date

  • February 15, 2019

Published In

Volume / Issue

  • 168 / 3

Start / End Page

  • 429 - 469

International Standard Serial Number (ISSN)

  • 0012-7094

Digital Object Identifier (DOI)

  • 10.1215/00127094-2018-0046

Citation Source

  • Scopus