Determinacy of determinantal varieties

Autor(es)

Ahmed, Imran ^[1] ; Soares Ruas, Maria Aparecida ^[2]

Afiliação do(s) autor(es)

^[1] COMSATS Inst Informat Technol, Dept Math, MA Jinnah Campus, Def Rd, Raiwind Rd, Lahore - Pakistan

^[2] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Comp, Ave Trabalhador Saocarlense 400, Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MANUSCRIPTA MATHEMATICA; v. 159, n. 1-2, p. 269-278, MAY 2019.
• Citações Web of Science: 0

Resumo

A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of an mxn-matrix. In this note, we consider G-finite determinacy of matrices defining a special class of determinantal varieties. They are called essentially isolated determinantal singularities (EIDS) and were defined by Ebeling and Gusein-Zade (Singul Appl 267:119-131, 2009). In this note, we prove that matrices parametrized by generic homogeneous forms of degree d define EIDS. It follows that G-finite determinacy of matrices holds in general. As a consequence, EIDS of a given type (m, n, t) holds in general. (AU)

• Processo FAPESP: 14/00304-2 - Singularidades de aplicações diferenciáveis: teoria e aplicações
• Beneficiário: Maria Aparecida Soares Ruas
• Modalidade de apoio: Auxílio à Pesquisa - Temático