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Note on the Formula for the Number of Quadrisecants of a Curve in Space of Three Dimensions

Published online by Cambridge University Press:  24 October 2008

Edwin A. Maxwell
Edwin A. Maxwell
Affiliation:
Queens' College
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Extract

If pCε is a curve of order ε and genus p without singularities in space of three dimensions, the formula for the number of quadrisecants is well known, namely*,

Welchman has shown that the necessary reduction in this formula when the curve pCε has a point of multiplicity r with r distinct tangents, no three of which are coplanar, is

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 3 , July 1935 , pp. 324 - 326
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

* E.g. Enriques-Chisini, , Teoria geometrica delle equazioni e delle funzioni algebriche, 3 (1924), 467–76.Google Scholar

† Welchman, W. G., Proc. Camb. Phil. Soc. 28 (1932), 206–8.CrossRefGoogle Scholar

‡ Val, P. Du, Proc. Lond. Math. Soc. (2), 39 (1935), 80.Google Scholar

* The value of p agrees with that obtained by use of the formula for the genus of the curve of intersection of two surfaces of orders m and n, having at a point O the respective multiplicities s and t, namely,