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Determination of the semi-nice dimensions

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
Affiliation:
Department of Pure Mathematics, University of Liverpool

Extract

As the culmination of a notable sequence of papers, Mather [6] gave a necessary and sufficient condition that stable maps were dense in C(N, P): it is that the dimensions n and p satisfy the condition n <σ(n, p), where σ(n, p) is the codimension (in a sufficiently large jet space) of the set of jets in Jr(n, p) whose classification (for ℋ-equivalence) ‘involves moduli’.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Briancon, J. and Galligo, A.. Déformations distinguées d'un point de ). Astérisque 7 (1973), 129138.Google Scholar
[2]Damon, J. N.. The classification of discrete algebra types, preprint (43 pp.), CUNY, 1973.Google Scholar
[3]Dimca, A. and Gibson, C. G.. Contact unimodular germs from the plane to the plane. Quart. J. Math. Oxford 34 (1983), 281295.Google Scholar
[4]Dimca, A. and Gibson, C. G.. Classification of equidimensional contact unimodular map-germs. Math. Scand., to appear.Google Scholar
[5]du Plessis, A. A.. Genericity and smooth finite determinacy. In Singularities, Proc. Symp. in Pure Math. vol. 40, part I (American Math. Soc, 1983), pp. 295312.Google Scholar
[6]Mather, J. N.. Stability of C mappings VI: the nice dimensions. Springer Lecture Notes in Math, vol. 192 (1971), 207253.CrossRefGoogle Scholar
[7]Mather, J. N.. Generic projections. Ann. of Math. 98 (1973), 226245.Google Scholar
[8]Wall, C. T. C.. Nets of conies. Math. Proc. Cambridge Philos. Soc. 81 (1977), 351364.Google Scholar
[9]Wall, C. T. C.. Finite determinacy of smooth map-germs. Bull. London Math. Soc. 13 (1981), 481539.Google Scholar
[10]Wall, C. T. C.. Classification of unimodal isolated singularities of complete intersections. In Singularities, Proc. Symp. in Pure Math vol. 40, part n (American Math. Soc., 1983) pp. 625640.Google Scholar