The Euler obstruction of a function on a determinantal variety and on a curve

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• 作者：D. A. H. Ament ; J. J. Nuño-Ballesteros…
• 关键词：determinantal singularity ; Euler obstruction ; Milnor number ; vanishing Euler characteristic
• 刊名：Bulletin of the Brazilian Mathematical Society
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：47
• 期：3
• 页码：955-970
• 全文大小：127 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1678-7714
• 卷排序：47

文摘

Given an analytic function germ f: (X, 0) → C on an isolated determinantal singularity or on a reduced curve, we present formulas relating the local Euler obstruction of f to the vanishing Euler characteristic of the fiber X ∩ f-1(0) and to the Milnor number of f. Restricting ourselves to the case where X is a complete intersection, we obtain an easy way to calculate the local Euler obstruction of f as the difference between the dimension of two algebras.