Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T19:50:47.491Z Has data issue: false hasContentIssue false

Combinants of a pencil of quadric surfaces (III)

Published online by Cambridge University Press:  24 October 2008

J. A. Todd
Affiliation:
Trinity CollegeCambridge

Extract

The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1948

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

* Todd, , Proc. Cambridge Phil. Soc. 43 (1947), 475, 488.CrossRefGoogle Scholar We shall refer to these papers as (I) and (II).

Turnbull, , Proc. London Math. Soc. (2), 18 (1919), 69.Google Scholar

Todd, , Proc. Cambridge Phil. Soc. 41 (1945), 127.CrossRefGoogle Scholar

* See § 4 of (I).

* The notation is as in (I). It is hoped that no confusion will occur between the α of (26) and αλ.

* The formulae are given in (47), (48), (49) of T.

* Compare Salmon, , Analytical Geometry of Three Dimensions (6th ed., Dublin, 1914), 248,Google Scholar and also § 9 of the paper T cited above [where, in (51), a term −γ23 γ31 γ12 has been omitted].