Nets of quadrics and deformations of \(\Sigma ^{3<3>}\) singularities. (English) Zbl 0698.57008
The 2-jet of a \(\Sigma^ 3\) map-germ \(({\mathbb{R}}^ 3,0)\to ({\mathbb{R}}^ 3,0)\) determines a net of quadratic maps from \({\mathbb{R}}^ 3\) to \({\mathbb{R}}^ 3\). The authors prove that the versal deformations of such map-germs representing nets of different classes (there are four of them) are topologically inequivalent.
Reviewer: I.V.Dolgačev
MSC:
57R45 | Singularities of differentiable mappings in differential topology |
58C25 | Differentiable maps on manifolds |
58K99 | Theory of singularities and catastrophe theory |
14C21 | Pencils, nets, webs in algebraic geometry |
Keywords:
\(\Sigma^ 3\) map germ; 2-jet; net of quadratic maps from \({\mathbb{R}}^ 3\) to \({\mathbb{R}}^ 3\); versal deformations; topologically inequivalentReferences:
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