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Rational normal octavic surfaces with a double line, in space of five dimensions

Published online by Cambridge University Press:  24 October 2008

D. W. Babbage
D. W. Babbage
Affiliation:
Magdalene College
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Extract

The following paper arises from a remark in a recent paper by Professor Baker. In that paper he gives a simple rule, under which a rational surface has a multiple line, expressed in terms of the system of plane curves which represent the prime sections of the surface. The rule is that, if one system of representing curves is given by an equation of the form

the surface being given, in space (x0, x1,…, xr), by the equations

then the surface contains the line

corresponding to the curve φ = 0; and if the curve φ = 0 has genus q, this line is of multiplicity q + 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 1 , January 1933 , pp. 95 - 102
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

* Baker, , “Note in regard to surfaces in space of four dimensions, in particular rational surfaces”, Proc. Camb. Phil. Soc. 28 (1932), 77.CrossRefGoogle Scholar

* Baker, , Principles of Geometry, vol. 4, 234.Google Scholar

† The quadrics of S 5 cut out a complete system of surfaces on the locus V 34.