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The geometry of the binary quintic form

Published online by Cambridge University Press:  24 October 2008

J. A. Todd
J. A. Todd
Affiliation:
Trinity CollegeCambridge
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Extract

1. It is familiar that the properties of the invariants and covariants of binary forms of the first four orders admit of elegant geometrical interpretations on rational normal curves and their projections. For forms of order higher than four the number of irreducible concomitants which appear in the complete system increases rapidly. It is the purpose of this note to exhibit geometrically the 23 irreducible concomitants of the binary quintic, using the rational normal curve R5 in space of five dimensions and its projection R′5 on to a prime as a foundation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 40 , Issue 1 , March 1944 , pp. 1 - 5
Copyright
Copyright © Cambridge Philosophical Society 1944

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References

* Grace, and Young, , Algebra of invariants (Cambridge, 1903), Ch. xiGoogle Scholar. We shall refer to this work as G. See also Telling, , The rational quartic curve in space of three and four dimensions (Cambridge Tracts in Mathematics and Physics, 34, 1936).Google Scholar

† For another representation of some of the covariants see Elliott, , Algebra of quantics (2nd ed. Oxford, 1913), p. 317.Google Scholar

* Unless O lies on R 5, which happens only when f is a perfect fifth power.

* For which see G. We use a, a′, a″, … as equivalent symbols belonging to the quintic

* G. p. 206; Telling, loc. cit.