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Affine cubic functions

I. The complex plane

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
University of Liverpool
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Extract

Although the classification of affine cubic curves was undertaken by Newton(4), in one of the first major exercises ever in coordinate geometry (see Cayley(2) for a fuller account), a parallel study of cubic functions seems not to have been contemplated till recently. The essential difference is that a function f defines a pencil of curves – its level curves – which have to be considered simultaneously. The author's interest in the subject arose from problems in singularity theory (concerning canonical stratifications), and a later paper in the series will have applications of this kind. Here we study the simplest case as an introduction. Our techniques are entirely classical, but the results are hard to find elsewhere. In later papers we intend to study cubic functions on ℝ2, and on ℂ3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 387 - 401
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

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