Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T22:28:20.647Z Has data issue: false hasContentIssue false
  • English
  • Français

Some loci in S5 associated with systems of conics in a plane

Published online by Cambridge University Press:  14 November 2011

A. J. Knight
A. J. Knight
Affiliation:
Mathematics Division, University of Sussex
Get access Rights & Permissions [Opens in a new window]

Synopsis

If the conic α, a0x2 + a1y2 + a2z2 + 2a3yz + 2a4zx + 2a5xy=0, is represented by the point (a0, a1, a2, a3, a4, a5) of S5, the transforms of α by projectivities that fix a second conic ω will generally be represented by points of a threefold in S5 containing (a0, a1,…, a5). It is shown that this threefold is in general a rational sextic belonging to an ∞2 family, that is composed of ∞1 sets of projectively equivalent threefolds. Special, exceptional members of the family are discussed.

Equations for the threefold are found in terms of the mutual projection invariants of ω and α.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 93 - 107
Copyright
Copyright © Royal Society of Edinburgh 1979

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

1Semple, J. G. and Roth, L.. Introduction to Algebraic Geometry (Oxford: Clarendon, 1949).Google Scholar
2Todd, J. A.. Projective and Analytical Geometry (New York: Pitman, 1946).Google Scholar
3Knight, A. J.. Conies related by a pentagram: a problem of J. E. Reeve. Proc. Roy. Soc. Edinburgh Sect. A 84, (1979), 109–115.CrossRefGoogle Scholar