Invariant of determinantal singularities and of maps on analytic varieties.
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP - Brazil
[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | MATHEMATICA SCANDINAVICA; v. 115, n. 2, p. 161-172, 2014. |
| Web of Science Citations: | 8 |
| Abstract | |
We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C-4, we obtain a Le-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the 1-form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from Fruhbis-Krtiger and Neumer {[}7] list of simple determinantal surface singularities. (AU) | |
| FAPESP's process: | 08/54222-6 - Singularities, geometry and differential equations |
| Grantee: | Maria Aparecida Soares Ruas |
| Support Opportunities: | Research Projects - Thematic Grants |