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Chern-Schwartz-MacPherson classes in the point of view of Obstruction Theory and Lipschitz framework

2025/02/11 by Jean‐Paul Brasselet, Brasselet, Jean-Paul, Tadeusz Mostowski +3
Engineering · #55R40 #55S35 #Advanced Research in Systems and Signal Processing #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2502.07567

openalex publication_date 2025/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since Chern and Grothendieck, Chern's characteristic class theory has made significant progress. In particular with regard to the classes of singular varieties. Conjectured by Grothendieck and Deligne and demonstrated by MacPherson, Chern classes of singular varieties have been defined in several ways, such as using polar varieties, Lagrangian theory... However, the initial definition using obstruction theory, due to Marie-Hélène Schwartz, has been forgotten. Despite the simple ideas that enabled the obstruction definition, their implementation using Whitney stratifications requires delicate and technical constructions. In the present article, we show that in the Lipschitz framework, the ideas of Marie-Hélène Schwartz lead to a simplified definition and construction of Chern classes of complex analytic varieties.

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