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A special Pencil of Binary Quartics

Published online by Cambridge University Press:  20 January 2009

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I. If the Jacobian sextic of a pencil of binary quartics is known, the pencil itself is determined in five ways. The explicit determination of the pencil in terms of the irrational invariants of has been effected by Stephanos.

There are two known cases in which a pencil of quartics admits of rational determination from its Jacobian. In these, the rationally determinable pencil differentiates itself algebraically from its remaining four co-Jacobian pencils.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1928

References

page 104 note 1 Mem. I'lnstitut, 27 (1883), 2.Google Scholar

page 104 note 2 The Null Pencil of Binary Quartics, Proc. Lond. Math. Soc., 2, 23 (1923) 317325.Google Scholar

page 106 note 1 This might be seen most simply by taking the two linearly independent members in the form

page 108 note 1 Compare Proc. L.M.S. loc. cit.Google Scholar

page 110 note 1 (For the theory of pedo-parallelism of inscribed triangles of a circle, see Proc. Camb. Phil. Soc. 23 (1926), p. 253.Google Scholar