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

By Jesse Leo Kass, K. Wickelgren. Duke mathematical journal, 2016

78 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1dd35844f4a2aa31c0690450a7031310f8d0931f

Citations in the corpus

• EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS (2020, unknown): “Proof. Immediate from [EHK+18, Proposition 4.3.17] (telling us that Morel’s transfer coincides with the one from §4.2.4) and Corollary B.4. Remark 8.6. Corollary 8.3(2) generalizes the main result of [KW19], at least for fields of characteristic 6= 2. Remark 8.7. We expect that all of the results in ”