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Regularity of the Segre stratification

Published online by Cambridge University Press:  24 October 2008

C. G. Gibson
C. G. Gibson
Affiliation:
University of Liverpool
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Extract

Arnol'd (1) remarks that the partition by Segre symbol of the endomorphisms of the complex vector space is a finite constructible stratification: in this paper we verify this statement, and show moreover that it is a Whitney stratification. Some of the arguments are by no means special to the case in hand; however, there seems little point in attempting a general formulation. It is a pleasure to acknowledge helpful conversations with Professor C. T. C. Wall and Dr E. J. N. Looijenga.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 91 - 97
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Arnol'd, V. I.On matrices depending on parameters. Uspehi Mat. Nauk 26 (1971), 101–114. (Russian Math. Surveys 26 (1971), 243.)Google Scholar
(2)Gantmacher, F. R.The theory of matrices (New York, Chelsea, 1969).Google Scholar
(3)Gibson, C. G. Construction of canonical stratifications. In Topological stability of smooth mappings (to appear).CrossRefGoogle Scholar
(4)Wall, C. T. C.Regular stratifications. Proceedings of the Warwick Symposium on Topology, 1974 (to appear).CrossRefGoogle Scholar
(5)Wirthmüller, K. Stratifications and flows. In Topological stability of smooth mappings (to appear).Google Scholar