Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T23:22:36.122Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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