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Maps of Certain Algebraic Curves Invariant under Cyclic Involutions of Periods Three, Five, and Seven

Published online by Cambridge University Press:  20 November 2018

W. R. Hutcherson  and
S. T. Gormsen
W. R. Hutcherson
Affiliation:
University of Florida
S. T. Gormsen
Affiliation:
University of Florida
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In earlier papers (4; 5; 6), certain space curves, invariant under cyclic involutions of periods three, five, and seven, have been mapped. Lucien Godeaux (2; 3) in 1916 mapped plane cubic curves, invariant under an involution of period three, onto a cubic surface in ordinary three-space. Mlle. J. Dessart (1) in 1931 mapped plane quintic curves, invariant under an involution of order five, onto a fifth order surface in a space of four dimensions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 92 - 98
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Dessart, J., Sur les surfaces représentant l'involution engendrée par une homographie de periode cinq du plan, Mem. Soc. Royale des Sciences de Liège (3), 17 (1931), 1–23.Google Scholar
2. Godeaux, M. L., Etude élémentaire sur Vhomographie plane de période trois et sur une surface cubique, Nouv. Ann. Math. (4), 16 (1916), 49–61.Google Scholar
3. Godeaux, M. L., Sur les homographies planes cycliques, Mem. Soc. Royale des Sciences de Liège, 15 (1930), 1–26.Google Scholar
4. Hutcherson, W. R., A cyclic involution of order seven, Bull. Amer. Math. Soc, 40 (1934), 143–151.Google Scholar
5. Hutcherson, W. R., Maps of certain cyclic involutions on two dimensional carriers, Bull. Amer. Math. Soc, 87 (1931), 759–765.Google Scholar
6. Hutcherson, W. R., Third order involution contained on a certain seventh degree surface (Abstract), Amer. Math. Monthly, 56 (1949), 586–587.Google Scholar