The class of Eisenbud–Khimshiashvili–Levine is the local A1-Brouwer degree
The class of Eisenbud–Khimshiashvili–Levine is the local A1-Brouwer degree
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Eisenbud-Khimshiashvili-Levine 的班级是当地的 A1-Brouwer 学位
DOI：
10.1215/00127094-2018-0046
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发表时间：
2016
影响因子：
2.5
通讯作者：
K. Wickelgren
中科院分区：
文献类型：
--
作者：
J. Kass;K. Wickelgren
给出一个零点在原点的多项式函数，我们证明了局部A1-Brouwer次等于Eisenbud-Khimshiashvili-Levine类。这回答了大卫·艾森巴德在1978年提出的一个问题。我们通过在Grothendieck-Witt群中丰富了局部梯度次数与超曲面奇点退化成的节点数之间的Milnor等式，给出了一个计算结点及其相关算术信息的应用。
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.