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15 February 2019 The class of Eisenbud–Khimshiashvili–Levine is the local A1-Brouwer degree
Jesse Leo Kass, Kirsten Wickelgren
Duke Math. J. 168(3): 429-469 (15 February 2019). DOI: 10.1215/00127094-2018-0046

Abstract

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.

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Jesse Leo Kass. Kirsten Wickelgren. "The class of Eisenbud–Khimshiashvili–Levine is the local A1-Brouwer degree." Duke Math. J. 168 (3) 429 - 469, 15 February 2019. https://doi.org/10.1215/00127094-2018-0046

Information

Received: 9 October 2017; Revised: 17 October 2018; Published: 15 February 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07040614
MathSciNet: MR3909901
Digital Object Identifier: 10.1215/00127094-2018-0046

Subjects:
Primary: 14F42
Secondary: 14B05, 55M25

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 3 • 15 February 2019
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