A remark on the Chern classes of local complete intersections
type: Item
instance of: scholarly article
title: A remark on the Chern classes of local complete intersections
zbMATH Open document ID: 0902.32017
author: Toru Ohmoto
author: Tatsuo Suwa
author: Shoji Yokura
published in: Proceedings of the Japan Academy. Series A
publication date: 1998-12-03T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 32S50
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 19L10
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 19E08
zbMATH DE Number: 1143829
zbMATH Keywords: isolated singularity
zbMATH Keywords: strong local complete intersection
zbMATH Keywords: polar multiplicity
zbMATH Keywords: Buchsbaum-Rim multiplicity
zbMATH Keywords: Nash blow-up
zbMATH Keywords: Milnor number
zbMATH Keywords: Chern-Mather class
zbMATH Keywords: Chern-Schwartz-MacPherson class
zbMATH Keywords: Fulton-Johnson's Chern class
zbMATH Keywords: Euler obstruction
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
full work available at URL: pjaa.73.93
OpenAlex ID: W2045865535
cites work: Singular schemes of hypersurfaces
cites work: Chern classes for singular hypersurfaces
cites work: Q3924846
cites work: Q4169000
cites work: Topological Radon transforms and the local Euler obstruction
cites work: Q3328651
cites work: Canonical classes on singular varieties
cites work: Multiplicities and equisingularity of ICIS germs
cites work: Der Gauß-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten
cites work: Lokale topologische Eigenschaften komplexer Räume
cites work: Index theorem for a maximally overdetermined system of linear differential equations
cites work: Residues of holomorphic vector fields relative to singular invariant subvarieties
cites work: Calculation of Milnor number of isolated singularity of complete intersection
cites work: Q3689276
cites work: Q3344082
cites work: Chern classes for singular algebraic varieties
cites work: AN ADJUNCTION FORMULA FOR LOCAL COMPLETE INTERSECTIONS
cites work: Classes de Chern des intersections complètes locales
cites work: Q3710626
DOI: 10.3792/PJAA.73.93
description: scientific article; zbMATH DE number 1143829