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The hyperosculating spaces to certain curves in [n]

Published online by Cambridge University Press:  20 January 2009

R. H. Dye
R. H. Dye
Affiliation:
School of Mathematics, University of Newcastle Upon Tyne
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Let Γ be an irreducible and non-singular curve in [n] (n ≧ 3) which is the complete intersection of n − 1 primals of order m (m ≧ 2) with a common “self-polar” simplex S: by this I mean that the rth polar of each vertex of S with respect to any one of the defining primals is the opposite face of S counted m−r times, for r = 1, 2, …, m − 1. The various such Γ constitute the curves of the title; they were encountered in (2). When m = 2, Γ is the intersection of n − 1 quadrics with a common self-polar simplex in the familiar classical sense.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 3 , March 1975 , pp. 301 - 309
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1) Baker, H. F., Principles of Geometry, Vols. 5, 6 (Cambridge, 1933).Google Scholar
(2) Dye, R. H., Osculating primes to curves of intersection in 4-space, and to certain curves in n-space, Proc. Edinburgh Math. Soc. (II) 18 (1973), 325–338.CrossRefGoogle Scholar
(3) Semple, J. G. and Kneebone, G. T., Algebraic Curves (Oxford, 1959).Google Scholar