| Full text | |
| Author(s): |
Lima-Pereira, B. K.
[1]
;
Nuno-Ballesteros, J. J.
[2, 3]
;
Orefice-Okamoto, B.
[1]
;
Tomazella, J. N.
[1]
Total Authors: 4
|
| Affiliation: | [1] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13560905 Sao Carlos, SP - Brazil
[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, PB - Brazil
[3] Univ Valencia, Dept Matemat, Campus Burjassot, Burjassot 46100 - Spain
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 64, n. 3, p. 662-674, AUG 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
We consider the relative Bruce-Roberts number mu((B) over barR)(f, X) of a function on an isolated hypersurface singularity (X, 0). We show that mu((B) over barR)(f, X) is equal to the sum of the Milnor number of the fibre mu(f(-1)(0) boolean AND X, 0) plus the difference mu(X, 0) - tau(X, 0) between the Milnor and the Tjurina numbers of (X, 0). As an application, we show that the usual Bruce-Roberts number mu(BR)(f, X) is equal to mu(f) + mu((B) over barR)(f, X). We also deduce that the relative logarithmic characteristic variety LC(X)(-), obtained from the logarithmic characteristic variety LC(X) by eliminating the component corresponding to the complement of X in the ambient space, is Cohen-Macaulay. (AU) | |
| FAPESP's process: | 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Projects - Thematic Grants |