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On isolated singularities of surfaces which do not affect the conditions of adjunction (Part I.)

Published online by Cambridge University Press:  24 October 2008

Patrick Du Val
Patrick Du Val
Affiliation:
Trinity College
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Extract

By an isolated singularity of an algebraic surface in [r] (i.e. space of r dimensions) I shall mean one which not merely is not upon any branch of a multiple curve of the surface, but has also the property that when the surface is projected into [3] from a general space [r − 4] the singular point remains in isolation, i.e. no branch of the double curve created by the projection will of necessity pass through it.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 30 , Issue 4 , October 1934 , pp. 453 - 459
Copyright
Copyright © Cambridge Philosophical Society 1934

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References

† Enriques, F. and Campedella, L., Lezioni sulla teoria delle superficie algebriche, § 39.Google Scholar

† Actually, Coxeter uses N 0, …, N n−1, etc., but the alteration introduced here seems to make for convenience.

‡ Salmon, , Analytical geometry of three dimensions, vol. 2 (1915), art. 522.Google Scholar

† Klein, Felix, Gesammelte mathematische Abhandlungen, 2, p. 11Google Scholar = Math. Ann. 6 (1873), 551.Google Scholar

‡ Enriques and Campedella, op. cit. § 59.

† Enriques and Campedella, op. cit. § 60.

† Coxeter, H. S. M., “The polytopes with regular prismatic vertex figures, Part 2,” Proc. Lond. Math. Soc. (2), 34 (1932), 126–189 (135–151).CrossRefGoogle Scholar

‡ See Coxeter, loc. cit. p. 137.