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Note on the trisecants and quadrisecants of a space curve

Published online by Cambridge University Press:  24 October 2008

W. G. Welchman
W. G. Welchman
Affiliation:
Sidney Sussex College.
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Extract

1. Formulae obtained by enumerative methods are always liable to break down owing to the appearance of an infinity of degenerate solutions, and when this happens it is usually necessary to make a fresh start. Enumerative arguments have been used to prove the two following results for a curve of order n and genus p in space of three dimensions:

(i) The order of the ruled surface formed by trisecant lines of the curve is

(ii) The number of quadrisecant lines is

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 2 , April 1932 , pp. 206 - 208
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

* See for instance Enriques, Teoria geometrica delle equazioni e delle funzioni algebriche, 3 (1924), pp. 472, 476.Google Scholar