| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | MATHEMATISCHE ANNALEN; NOV 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 14/00304-2 - Singularities of differentiable mappings: theory and applications |
| Grantee: | Maria Aparecida Soares Ruas |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 15/04409-6 - On the classification and topology of singularities |
| Grantee: | Roberta Godoi Wik Atique |
| Support Opportunities: | Regular Research Grants |