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:
| [1] | Wall, Compositio Math. 42 pp 187– (1981) |
| [2] | DOI: 10.1098/rsta.1978.0060 · Zbl 0382.14011 · doi:10.1098/rsta.1978.0060 |
| [3] | Wall, Math. Proc. Cambridge Philos. Soc. 81 pp 351– (1977) |
| [4] | DOI: 10.1007/BF01389958 · Zbl 0333.57017 · doi:10.1007/BF01389958 |
| [5] | Hellebrand, Regensburger Math. Schriften 9 (1985) |
| [6] | Damon, Compositio Math. 47 pp 101– (1982) |
| [7] | DOI: 10.2307/2374137 · Zbl 0498.58005 · doi:10.2307/2374137 |
| [8] | Ronga, C. R. Acad. Sci. Paris S?r. I Math. 287 pp 779– (1978) |
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