Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 42

Research Article

The Linear Complexes belonging to the Invariant System of Three Quadrics

J. Williamson

In the Proceedings of the London Mathematical Society, Ser. 2, Vol. 20 (1921), pp. 465–489, Professor H. W. Turnbull has studied the projective invariant theory of three quadrics. The following paper is based on this work and develops one definite section of the theory. From the geometrical point of view the linear complex is now seen to be fundamental in the study of three arbitrary quadrics; particularly when their (2, 2, 2) invariant φ123 vanishes.

(Received January 23 1923)

(Revised January 11 1923)

Notes

* φ123=0 when the three quadrics can be expressed as the sum of the same five squares (Toeplitz, Math. Annal., XI.)

* Cf. Proc. Lond. Math. Soc., loc. cit., p. 483. Type 9 on this table is reducible. Proc. Land. Math. Soc. Vol. 22. Series 2. Records p. iii. (1923).

* This denotes that the form is reducible.