Caps on Classical Varieties and their Projections
Document Type
Article
Publication Date
2-2001
Department
Department of Mathematical Sciences
Abstract
A family of caps constructed by G. L. Ebert, K. Metsch and T. Szönyi [8] results from projecting a Veronesian or a Grassmannian to a suitable lower-dimensional space. We improve on this construction by projecting to a space of much smaller dimension. More precisely, we partition PG(3r - 1, q) into a (2r - 1)-space, an (r - 1)-space and qr - 1 cyclic caps, each of size (q2r - 1)/(q - 1). We also decide when one of our caps can be extended by a point from the (2r - 1)-space or the (r - 1)-space. The proof of the results uses several ingredients, most notably hyperelliptic curves.
Publication Title
European Journal of Combinatorics
Recommended Citation
Bierbrauer, J.,
Cossidente, A.,
&
Edel, Y.
(2001).
Caps on Classical Varieties and their Projections.
European Journal of Combinatorics,
22(2), 135-143.
http://doi.org/10.1006/eujc.2000.0457
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3944
