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An aspect of the invariant of degree 4 of the binary quintic

Published online by Cambridge University Press:  20 January 2009

W. L. Edge
W. L. Edge
Affiliation:
Montague House, 67 Mill Hill Musselburgh, EH21 7RLScotland
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A binary form of odd degree,

has a quadratic covariant Г, (ab2maxbx in Aronhold's notation, and the discriminant Δ of Г is an invariant of ƒ For m = 2Δ was obtained by Cayley in 1856 [3, p. 274]; it was curiosity as to how Δ could be interpreted geometrically that triggered the writing of this note. An interpretation, in projective space [2m + 1], that does not seem to be on record, of Γ and Δ is found below. If m = 1 one has merely the Hessian and discriminant of a binary cubic whose interpretations in the geometry of the twisted cubic are widely known [5, pp. 241–2].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 133 - 140
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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