CODIMENSION TWO DETERMINANTAL VARIETIES WITH ISOLATED SINGULARITIES

Author(s)

Soares Ruas, Maria Aparecida ^[1] ; Pereira, Miriam Da Silva ^[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

• 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