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Configurations defined by six lines in space of three dimensions

Published online by Cambridge University Press:  24 October 2008

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

The investigations which follow were originally suggested by the now classical problem of Cayley, the determination of the condition that seven lines in space, of which no two intersect, should lie on a quartic surface. This problem suggests the consideration of the linear system of quartic surfaces which pass through six given lines, and this, essentially, is the basis of all that follows.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 1 , January 1933 , pp. 52 - 68
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

REFERENCES

(1)Baker, H. F., Principles of geometry (Cambridge), 3 (1923), 4 (1924).Google Scholar
(2)Coble, A. B., Algebraic geometry and theta-functions (New York, 1929).Google Scholar
(3)Hudson, H. P., Cremona transformations (Cambridge, 1927).Google Scholar
(4)Montesano, D., “Su le transformazioni involutorie dello spazio che determinano un complesso lineare di rette”, Rend. Acc. Lincei (4), 4 1 (1888), 207–215.Google Scholar
(5)Pieri, M., “Formule di coincidenza per la serie algebriche di coppie di punti dello spazio a n dimensioni”, Rend. di Palermo, 5 (1891), 252–268.CrossRefGoogle Scholar
(6)Reye, T., “Über lineare Mannigfaltigkeiten projectiver Ebenenbüschel und collinearer Bündel oder Raüme, V”, Journ. für Math. 108 (1891), 89–102.Google Scholar
(7)Richmond, H. W., “On Cayley's problem of seven lines”, Journ. London Math. Soc. 7 (1932), 113–117.CrossRefGoogle Scholar
(8)Room, T. G., “An extension of the theorem of the fifth associated line”, Proc. London Math. Soc. (2), 31 (1931), 455–486.Google Scholar
(9)Roth, L., “A quartic form in four dimensions”, Proc. London Math. Soc. (2), 30 (1930), 118–126.CrossRefGoogle Scholar
(10)Schubert, H., “Die n-dimensionale Verallgemeinerung der Anzahlen für die vielpunktig berührenden Tangenten einer punktallgemeinen Fläche n-ten Grades”, Math. Ann. 26 (1886), 52–73.CrossRefGoogle Scholar
(11)Ursell, H. D., “Cayley's problem of seven lines on a quartic surface”, Proc. Camb. Phil. Soc. 25 (1929), 31–38.CrossRefGoogle Scholar
(12)Wakeford, E. K., “Chords of twisted cubics”, Proc. London Math. Soc. (2), 21 (1923), 89–113.Google Scholar