Skip to main content Accessibility help
×
Home

Hermitian Varieties in a Finite Projective Space PG(N, q 2)

  • R. C. Bose (a1) and I. M. Chakravarti (a1)

Extract

The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another class of varieties, which we call Hermitian varieties and which have many properties analogous to quadrics. Hermitian varieties are defined only for finite projective spaces for which the ground (Galois field) GF(q 2) has order q2, where q is the power of a prime. If h is any element of GF(q2), then = hq is defined to be conjugate to h.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Hermitian Varieties in a Finite Projective Space PG(N, q 2)
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Hermitian Varieties in a Finite Projective Space PG(N, q 2)
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Hermitian Varieties in a Finite Projective Space PG(N, q 2)
      Available formats
      ×

Copyright

References

Hide All
1. Baer, R., Linear algebra and projective geometry (New York, 1952).
2. Bose, R. C., On the construction of balanced incomplete block designs, Ann. Eugen. London, 9 (1939), 358399.
3. Bose, R. C., On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements, Golden jubilee commem. vol., Cal. Math. Soc. (1958-59), 341354.
4. Bose, R. C., Strongly regular graphs, partial geometries and partially balanced designs, Pacific J. Math., 13 (1963), 389419.
5. Bose, R. C., Combinatorial properties of partially balanced designs and association schemes, Sankhya, ser. A, 25 (1963), 109136; and Contributions to statistics, presented to Professor P. C. Mahalanobis on the occasion of his 70th birthday (Calcutta, 1964), 21-48.
6. Bose, R. C. and Clatworthy, W. H., Some classes of partially balanced designs, Ann. Math. Statist., 26 (1955), 212232.
7. Bose, R. C. and Mesner, D. M., On linear associative algebras corresponding to association schemes of partially balanced designs, Ann. Math. Statist., 30 (1959), 2138.
8. Bose, R. C. and Nair, K. R., Partially balanced incomplete block designs, Sankhya, 4 (1939), 337372.
9. Bose, R. C. and Shimamoto, T., Classification and analysis of partially balanced designs with two associate classes, J. Amer. Statist. Assoc, 47 (1952), 151184.
10. Carmichael, R., Introduction to the theory of groups of finite order (New York, 1956), chaps. XI and XII.
11. Mann, H. B., Analysis and design of experiments (New York, 1949). chap. IX.
12. Primrose, E. J. F., Quadrics infinite geometries, Proc. Cambridge Philos. Soc., 47 (1951), 299304.
13. Ray-Chaudhuri, D. K., Some results on quadrics infinite projective geometries based on Galois fields, Can. J. Math., 14 (1962), 129138.
14. Ray-Chaudhuri, D. K., Application of the geometry of quadrics for constructing PBIB designs, Ann. Math. Statist., 33 (1962), 11751186.
15. Segre, B., Lectures on modern geometry (Rome, 1960). chap. 17.
16. Shrikhande, S. S. and Singh, N. K., On a method of constructing symmetrical balanced incomplete block designs, Sankhya, ser. A, 24 (1962), 2532.
17. Takeuchi, K., On the construction of a series of BIB designs, Statist. Appl. Res., JUSE, 10 (1963), 48.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Hermitian Varieties in a Finite Projective Space PG(N, q 2)

  • R. C. Bose (a1) and I. M. Chakravarti (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed