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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

CODIMENSION TWO DETERMINANTAL VARIETIES WITH ISOLATED SINGULARITIES

Author(s):
Soares Ruas, Maria Aparecida [1] ; Pereira, Miriam Da Silva [2]
Total Authors: 2
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
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 type: Research Projects - Thematic Grants