Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-23T18:04:42.967Z Has data issue: false hasContentIssue false
  • English
  • Français

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: ton@icmc.usp.br
J. J. NUÑO–BALLESTEROS
Affiliation:
Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100 Burjassot, Spain. e-mail: juan.nuno@uv.es
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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