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Harmonic tetrads and harmonic elliptic quartic curves

Published online by Cambridge University Press:  14 February 2012

R. H. Dye
R. H. Dye
Affiliation:
Department of Mathematics, University of Newcastle upon Tyne
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Synopsis

The group of a harmonic elliptic quartic has exceptional action on the edges of the self-polar tetrahedron, singling out one pair of opposite edges. Geometrical explanations are given. One concerns the possession by each of these two edges of a certain harmonic tetrad constructible in three ways. The same constructions yield, for a general quartic, three distinct tetrads on each edge of its tetrahedron, with a related fourth. The cases of exceptional overlap of these tetrads are examined: they occur for quartics of moduli 0, ∞ and — 32/49.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 91 - 96
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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