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Humbert's plane sextics of genus 5

Published online by Cambridge University Press:  24 October 2008

W. L. Edge
W. L. Edge
Affiliation:
Mathematical Institute16 Chambers StreetEdinburgh 1
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Extract

1. In 1894 Humbert encountered a twisted curve C7, of order 7 and genus 5, the locus of points of contact of tangents from a fixed point N0 to those twisted cubics which pass through five fixed points N1, N2, N3, N4, N5. The cubics of this family which touch an arbitrary plane do so at points on a conic, and it was by investigating this complex of conics that Humbert was led to study C7.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 483 - 495
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

* École, J.. Polytech., Paris 64 (1894), 123–49.Google Scholar

† Multiply periodic functions (Cambridge, 1907), pp. 162 and 322–6.Google Scholar Baker was apparently then unaware that the curve had been found earlier, but in Principles of geometry, 6 (Cambridge, 1933), 24,Google Scholar he duly gives the reference to Humbert.

† Baker, , Principles of geometry, 5 (Cambridge, 1933), 239.Google Scholar

* Segre, C., ‘Intorno ai punti di Weierstrass di una curva algebrica’, Rend. Accad. Lincei, 8 2 (1899), 89–91.Google Scholar

* Math. Ann. 24 (1884), 339.Google Scholar