## The class of Eisenbud-Khimshiashvili-Levine is the local A ^{1} -Brouwer degree

Publication
, Journal Article

Kass, JL; Wickelgren, K

Published in: Duke Mathematical Journal

February 15, 2019

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.

### Duke Scholars

##### Altmetric Attention Stats

##### Dimensions Citation Stats

## Published In

Duke Mathematical Journal

## DOI

## ISSN

0012-7094

## Publication Date

February 15, 2019

## Volume

168

## Issue

3

## Start / End Page

429 / 469

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Kass, J. L., & Wickelgren, K. (2019). The class of Eisenbud-Khimshiashvili-Levine is the local A

^{1}-Brouwer degree.*Duke Mathematical Journal*,*168*(3), 429–469. https://doi.org/10.1215/00127094-2018-0046Kass, J. L., and K. Wickelgren. “The class of Eisenbud-Khimshiashvili-Levine is the local A

^{1}-Brouwer degree.”*Duke Mathematical Journal*168, no. 3 (February 15, 2019): 429–69. https://doi.org/10.1215/00127094-2018-0046.Kass JL, Wickelgren K. The class of Eisenbud-Khimshiashvili-Levine is the local A

^{1}-Brouwer degree. Duke Mathematical Journal. 2019 Feb 15;168(3):429–69.Kass, J. L., and K. Wickelgren. “The class of Eisenbud-Khimshiashvili-Levine is the local A

^{1}-Brouwer degree.”*Duke Mathematical Journal*, vol. 168, no. 3, Feb. 2019, pp. 429–69.*Scopus*, doi:10.1215/00127094-2018-0046.Kass JL, Wickelgren K. The class of Eisenbud-Khimshiashvili-Levine is the local A

^{1}-Brouwer degree. Duke Mathematical Journal. 2019 Feb 15;168(3):429–469.## Published In

Duke Mathematical Journal

## DOI

## ISSN

0012-7094

## Publication Date

February 15, 2019

## Volume

168

## Issue

3

## Start / End Page

429 / 469

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics