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Note on the invariant of plane cubics

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

It was noted by Klein(4), part I, ch. II, §9, that if a polyhedral group G acts on the 2-sphere identified with P1(ℂ), then the polynomials cΠg∈G(λ − ag μ) form, as a∈ℂ varies, a vector space of dimension 2 over ℂ. G is generated by elements T1, T2 fixing respectively a vertex and a face; T1T2 fixes an edge and these elements have orders p, q, 2 where 1/p + 1/q > ½ Taking a to be a vertex or the mid-point of a face or an edge yields polynomials of the form and which are thus linearly dependent. The ring of all (relatively) invariant polynomials is generated by F1F2 and F3 subject to this single relation.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 3 , May 1979 , pp. 403 - 406
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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