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The normal rational septimic surface with two skew double lines in space of four dimensions

Published online by Cambridge University Press:  24 October 2008

J. Bronowski
J. Bronowski
Affiliation:
Jesus College.
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Extract

1. The surface here discussed arises most naturally in the study of a certain cubic primal in space of five dimensions. Let G be a cubic primal in five-dimensional space, containing two planes M1, M2 which do not intersect. From any point of G can be drawn one transversal to M1, M2; this does not meet G again, and meets a fixed prime p in one point. Thus G can be birationally projected upon p, and is rational.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 4 , 30 October 1933 , pp. 478 - 483
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

† Babbage, D. W., Proc. Camb. Phil. Soc. 29 (1933), 95–102 and 405–6.CrossRefGoogle Scholar See also Baker, H. F., Proc. Camb. Phil. Soc. 28 (1932), 79CrossRefGoogle Scholar, and Roth, L., Proc. Camb. Phil. Soc. 29 (1933), 186–87.Google Scholar

* There exists another normal rational septimic surface f′ of four-dimensional space with two double lines, the projection from a simple point of itself of the surface F 8(5) with a double line given by L. Roth, loc. cit. 187, and D. W. Babbage, loc. cit. 405. But the double lines of f′ are concurrent, as may be seen from its plane representation by novenic curves with eight triple and two simple base-points.