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arXiv · 1608.05669

The class of Eisenbud--Khimshiashvili--Levine is the local A1-Brouwer degree

Jesse Leo Kass·Kirsten Wickelgren
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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 degenerates to an equality in the Grothendieck-Witt group.

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Jesse Leo Kass, Kirsten Wickelgren. 2016-08-19. The class of Eisenbud--Khimshiashvili--Levine is the local A1-Brouwer degree. https://doi.org/10.1215/00127094-2018-0046

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