Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T07:15:31.979Z Has data issue: false hasContentIssue false
  • English
  • Français

Complete quadrics and collineations in Sn

Published online by Cambridge University Press:  26 February 2010

J. A. Tyrrell
J. A. Tyrrell
Affiliation:
King's College, London.
Get access

Extract

In this paper we shall set out the generalization, for n-dimensional space Sn, of some recent results about complete quadrics and complete collineations in S2, S3 and S4. For the results about complete conies in S2, originally introduced by Study [1], we refer the reader to papers by Severi ([2], [3]), van der Waerden [4], Semple [5]; for those about complete quadrics in S3, to Semple ([6], [7]); for the extension to S4 to Alguneid [8]; for the general concept of complete collineations in Sn, and for results in S2 and S3, to Semple [9].

Type
Research Article
Information
Mathematika , Volume 3 , Issue 1 , June 1956 , pp. 69 - 79
Copyright
Copyright © University College London 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Study, E., “Über die Geometrie der Kegelschnitte, insbesondere deren Charakteristiken-problem”, Math. Annalen 26 (1886), 58–101.CrossRefGoogle Scholar
2.Severi, F., “Sui fondamenti della geometria numerativa e sulla teoria delle caratter-istiche”, Atti. del R. 1st. Veneto 75 (1916), 1122–1162.Google Scholar
3.Severi, F., “I fondamenti della geometria numerativa”, Ann. di Mat. (4), 19 (1940), 151–242.Google Scholar
4.Waerden, B. L. van der, “Z.A.G. XV. Lösung des Charakteristikenproblems für Kegelschnitte”, Math. Annalen 115 (1938), 645–655.CrossRefGoogle Scholar
5.Semple, J. G., “Note on Halphen conditions”, Journal London Math. Soc. 26 (1951), 122–125.CrossRefGoogle Scholar
6.Semple, J. G., “On complete quadrics (I)”, Journal London Math. Soc. 23 (1948), 258–267.CrossRefGoogle Scholar
7.Semple, J. G., “On complete quadrics (II)”, Journal London Math. Soc. 27 (1952), 280–287.CrossRefGoogle Scholar
8.Alguneid, A. R., “Complete quadric primals in four-dimensional space”, Proc. Math. Phys. Soc. Egypt. 4 (1952), No. 4, 93–104 (1953).Google Scholar
9.Semple, J. G., “The variety whose points represent complete collineations of Sr on Sr'”, Rend, di Mat. Univ. Roma (5), 10 (1951), 201–208.Google Scholar
10.MacDuffee, C. C., Theory of Matrices (Berlin, 1933).CrossRefGoogle Scholar
11.Hodge, W. V. D. and Pedoe, D., Methods of Algebraic Geometry, Volume II (Cambridge, 1952).Google Scholar
12.Schubert, H., Kalkül der Abzählenden Geometrie (Leipzig, 1879).Google Scholar