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The Linear Complexes belonging to the Invariant System of Three Quadrics

Published online by Cambridge University Press:  20 January 2009

J. Williamson
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , February 1923 , pp. 29 - 40
Copyright
Copyright © Edinburgh Mathematical Society 1923

References

* 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.