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A note on finite determinacy for corank 2 map germs from surfaces to 3-space

Published online by Cambridge University Press:  01 July 2008

W. L. MARAR  and
J. J. NUÑO–BALLESTEROS
W. L. MARAR
Affiliation:
Universidade de São Paulo - ICMC, Caixa Postal 668, 13560-970 São Carlos (SP), Brazil. e-mail: [email protected]
J. J. NUÑO–BALLESTEROS
Affiliation:
Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100 Burjassot, Spain. e-mail: [email protected]
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Abstract

We study properties of finitely determined corank 2 quasihomogeneous map germs f:(, 0) → (, 0). Examples and counter examples of such map germs are presented.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 153 - 163
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

[1]Arnold, V. I.. Singularités des applications différentiables, vol. I, (Editions Mir, 1986).Google Scholar
[2]Bruce, J. W. and Marar, W. L.. Images and varieties, Topology, 3. J. Math. Sci. 82 (1996), 3633–3641.CrossRefGoogle Scholar
[3]Bruce, J. W., Ruas, M. A. S. and Saia, M.. A note on determinacy. Proc. Amer. Math. Soc. 115, no. 3 (1992), 865–871.CrossRefGoogle Scholar
[4]Marar, W. L. and Mond, D.. Multiple point schemes for corank 1 maps. J. London Math. Soc. 39 (1989), 553–567.CrossRefGoogle Scholar
[5]Milnor, J. and Orlik, P.. Isolated singularities defined by weighted homogeneous polynomials. Topology 9 (1970), 385–393.CrossRefGoogle Scholar
[6]Mond, D.. Some remarks on the geometry and classification of germs of maps from surfaces to 3-space. Topology 26 (1987), 361–383.CrossRefGoogle Scholar
[7]Mond., D.The number of vanishing cycles for a quasihomogeneous mapping from to . Quart. J. Math. Oxford (2), 42 (1991), 335–345.CrossRefGoogle Scholar
[8]Mond, D. and Pellikaan, R.. Fitting ideals and multiple points of analytic mappings. Lecture Notes in Math. 1414 (Springer, 1989), 107–161.CrossRefGoogle Scholar
[9]Mond, D.. Vanishing cycles for analytic maps. Lecture Notes in Math. 1462 (Springer, 1991), 221–234.CrossRefGoogle Scholar
[10]Piene, R.. Ideals associated to a desingularization. Lecture Notes in Math. 732 (Springer, 1979) 503–517.CrossRefGoogle Scholar
[11]Wall, C. T. C.. Finite determinacy of smooth map-germs. Bull. London. Math. Soc. 13 (1981), 481–539.CrossRefGoogle Scholar