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A family of quadrics
Published online by Cambridge University Press: 20 January 2009
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In a recent paper I have discussed the families of quadrics in [2n] which are obtained by causing the members to have the greatest possible number of fixed [n – 1]'s or “generators.” It was found possible to fix four [n – 1]'s in general position; the family of quadrics through these possessed a “base” variety, common to all the members, which consisted of a highly degenerate Vn–1. Here I consider the same problem for quadrics in [2n + 1], find how many generators may be assigned arbitrarily and discuss the common part of the quadrics which pass through such generators.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 5 , Issue 4 , September 1938 , pp. 207 - 210
- Copyright
- Copyright © Edinburgh Mathematical Society 1938
References
page 207 note 1 Brown, L. M., Proc. Edinburgh Math. Soc. (2), 5 (1938), 125.CrossRefGoogle Scholar
page 207 note 2 See in particular Room, T. G., Proc. London Math. Soc. (2), 36 (1933), 1.Google Scholar In the notation of that paper the base variety is) | n + 1, 2 |, [2n + 1](.
page 208 note 1 See Richmond, H. W. and Bath, F., Proc. Cambridge Phil. Soc., 22 (1924), 319CrossRefGoogle Scholar, where a bibliography is given; in our connection see in particular two papers by Segre, C., Rend, di Palermo, 5 (1891), 192 and 30 (1910), 87.CrossRefGoogle Scholar
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