Proceedings of the Edinburgh Mathematical Society (Series 2)
- Proceedings of the Edinburgh Mathematical Society (Series 2) / Volume 29 / Issue 01 / February 1986, pp 133-140
- Copyright © Edinburgh Mathematical Society 1986
- DOI: http://dx.doi.org/10.1017/S0013091500017491 (About DOI), Published online: 20 January 2009
Research Article
An aspect of the invariant of degree 4 of the binary quintic
W. L. Edgea1
a1 Montague House, 67 Mill Hill Musselburgh, EH21 7RL Scotland
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].
(Received May 31 1985)
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