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On elliptic quartic curves with assigned points and chords

Published online by Cambridge University Press:  24 October 2008

W. G. Welchman
W. G. Welchman
Affiliation:
Sidney Sussex College
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Extract

1. The problem which I propose to solve is that of finding the number of quartic curves of intersection of two quadrics which pass through p points and have q lines as chords, where p + q = 8. There are ∞16 elliptic quartics in space; to contain a line as a chord is two conditions, and to pass through a point is two conditions, so we should expect a finite number of solutions. Throughout this paper I shall refer to an elliptic quartic curve in space of three dimensions simply as a “quartic.” I shall denote the number of solutions for a particular value of p by np.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 1 , January 1931 , pp. 20 - 23
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

* See Segre, , “Mehrdimensionale Räume,” Encykl. Math. Wiss., III c, 7, 815.Google Scholar