Equivariant characteristic classes of singular hypersurfaces
In this paper, we introduce definitions for the integrated equivariant Milnor number μIG and the equivariant Milnor class ℳG(Z), for singular hypersurfaces. We prove that the μIG are constant on the strata in a Whitney stratification of Z, along with the correlation ℳG(Z) = ℳG,0(Z) = 1 |G|Σi=1kμ IG(...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/302649 |
| Acceso en línea: | http://dx.doi.org/10.1142/S0129167X24500782 https://hdl.handle.net/11449/302649 |
| Access Level: | acceso abierto |
| Palabra clave: | Equivariant characteristic classes Milnor number singular hypersurfaces |
| Sumario: | In this paper, we introduce definitions for the integrated equivariant Milnor number μIG and the equivariant Milnor class ℳG(Z), for singular hypersurfaces. We prove that the μIG are constant on the strata in a Whitney stratification of Z, along with the correlation ℳG(Z) = ℳG,0(Z) = 1 |G|Σi=1kμ IG(x i) for hypersurfaces hosting isolated singularities x1,...,xk, where ℳG,0(Z) denotes the 0th equivariant Milnor class of Z. We also introduce the equivariant Fulton-Johnson class of singular hypersurfaces. We give an equivariant version of Verdier's specialization morphism in homology, and also for constructible functions. This is used for finding a relation between equivariant Fulton-Johnson and Schwartz-MacPherson classes. |
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