| Full text | |
| Author(s): |
Grulha Jr, N. G.
;
Monteiro, A.
;
Morgado, M. F. Z.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL OF MATHEMATICS; v. 36, n. 03, p. 24-pg., 2024-11-26. |
| Abstract | |
In this paper, we introduce definitions for the integrated equivariant Milnor number mu(G)(I) and the equivariant Milnor class M-G(Z), for singular hypersurfaces. We prove that the mu(G)(I) are constant on the strata in a Whitney stratification of Z, along with the correlation M-G(Z) = M-G,M-0(Z) = 1/vertical bar G vertical bar Sigma(k)(i=1) mu(G)(I)(x(i)) for hypersurfaces hosting isolated singularities x(1),..., x(k), where M-G,M-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. (AU) | |
| FAPESP's process: | 19/21181-0 - New frontiers in Singularity Theory |
| Grantee: | Regilene Delazari dos Santos Oliveira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 23/01649-2 - Singularities of maps, characteristic classes, and intersection homology |
| Grantee: | Nivaldo de Góes Grulha Júnior |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 19/02068-8 - Equivariant characteristic classes of singular hypersurfaces |
| Grantee: | Amanda Monteiro |
| Support Opportunities: | Scholarships in Brazil - Doctorate |