Chern-Schwartz-MacPherson classes in the point of view of Obstruction Theory and Lipschitz framework
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| Format: | Preprint |
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2025
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| _version_ | 1866915146167746560 |
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| author | Brasselet, Jean-Paul Mostowski, Tadeusz Bich, Thuy Nguyen Thi |
| author_facet | Brasselet, Jean-Paul Mostowski, Tadeusz Bich, Thuy Nguyen Thi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_07567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern-Schwartz-MacPherson classes in the point of view of Obstruction Theory and Lipschitz framework Brasselet, Jean-Paul Mostowski, Tadeusz Bich, Thuy Nguyen Thi Algebraic Geometry Algebraic Topology 55R40, 55S35 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. |
| title | Chern-Schwartz-MacPherson classes in the point of view of Obstruction Theory and Lipschitz framework |
| topic | Algebraic Geometry Algebraic Topology 55R40, 55S35 |
| url | https://arxiv.org/abs/2502.07567 |