The extra-nice dimensions

Autor(es)

Sinha, R. Oset ^[1] ; Ruas, M. A. S. ^[2] ; Atique, R. Wik ^[2]

Afiliação do(s) autor(es)

^[1] Univ Valencia, Dept Matemat, Campus Burjassot, Burjassot 46100 - Spain

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Av Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATISCHE ANNALEN; NOV 2021.
• Citações Web of Science: 0

Resumo

We define the extra-nice dimensions and prove that the subset of locally stable 1-parameter families in C-infinity (N x {[}0, 1], P) is dense if and only if the pair of dimensions (dim N, dim P) is in the extra-nice dimensions. This result is parallel to Mather's characterization of the nice dimensions as the pairs (n, p) for which stable maps are dense. The extra-nice dimensions are characterized by the property that discriminants of stable germs in one dimension higher have A(e)-codimension 1 hyperplane sections. They are also related to the simplicity of A(e)-codimension 2 germs. We give a sufficient condition for any A(e)-codimension 2 germ to be simple and give an example of a corank 2 codimension 2 germ in the nice dimensions which is not simple. Then we establish the boundary of the extra-nice dimensions. Finally we answer a question posed by Wall about the codimension of non-simple maps. (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
• Processo FAPESP: 15/04409-6 - Classificação e topologia das singularidades
• Beneficiário: Roberta Godoi Wik Atique
• Modalidade de apoio: Auxílio à Pesquisa - Regular