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Some enumerative results for elliptic quartic curves

Published online by Cambridge University Press:  24 October 2008

J. A. Todd
J. A. Todd
Affiliation:
Trinity College
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Extract

In a recent paper Mr W. G. Welchman has devised an extremely simple method for determining the number of elliptic quartic curves in space which pass through p given points and have 8–p assigned lines as chords. In the present note this method will be applied, with certain necessary extensions, to some cases in which the curves are subject to the condition of meeting certain lines in one point only, in addition to conditions of the previous type. The method in principle is perfectly straightforward, but circumstances arise which make its application somewhat limited.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 4 , October 1931 , pp. 538 - 542
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

* Welchman, , Proc. Camb. Phil. Soc. 27 (1931), 20.CrossRefGoogle Scholar

* Giambelli, , Mem. di Torino (2), 52 (1902), 171Google Scholar; cf. Segre, , Encyk. der Mat. Wiss. iii C 7, 818.Google Scholar

* Welchman, loc. cit.

† van Kol, , Proc. Acad. Sci., Amsterdam, 32 (1929), 231Google Scholar; ibid. 495; Nieuw Archief v. Wisk., Amsterdam, 16 (1929), 92.