A remark on the Chern classes of local complete intersections
Let \(X\) be an \(n\)-dimensional compact analytic variety with isolated singularities \(p_1, \ldots, p_r \in X.\) Assume additionally that \(X\) is a strong local complete intersection in the sense [\textit{D. Lehmann} and \textit{T. Suwa}, J. Differ. Geom. 42, 165-192 (1995; Zbl 0844.32007)]. The authors show that the difference between the Chern-Mather and Fulton-Johnson's Chern classes of \(X\) is equal to \((-1)^{n+1}\sum_{i=1}^r m_n(X,p_i),\) where \(m_n(X,p_i)\) is the \(n\)-th polar multiplicity of \(X\) at the singular point \(p_i\), \(i=1,\dots, r\). The prove is based essentially on results of \textit{T. Suwa} [C. R. Acad. Sci., Paris, Sér. I 324, No. 1, 67-70 (1997)] and \textit{L. Ernström} [Duke Math. J. 76, 1-21 (1994; Zbl 0831.32016)].
scientific article; zbMATH DE number 1143829
scientific article