The Maximum Number of Double Points on a Surface

descriptionPublicationkeyboard_double_arrow_right Article 11 Jan 1906 English Publisher:Springer Science and Business Media LLCJournal:Nature, volume 73, pages 246-246 (issn: 0028-0836, eissn: 1476-4687,

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Authors: Basset, A. B.;

doi: 10.1038/073246b0

The Maximum Number of Double Points on a Surface

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Abstract

IT is obvious that a surface, like a curve, must have a maximum number of double points; and it is also obvious that all of them may be conic nodes, but only a limited number of them can be binodes; but so far as I have been able to discover, no formula has been obtained for determining the maximum number. In Hudson's book on “Kummer's Surface,” a proof is given that a quartic surface can have as many as sixteen conic nodes, but no general theorem is alluded to. I shall therefore state a formula by means of which the maximum number can be calculated.

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