Caps on Classical Varieties and their Projections
✍ Scribed by Jürgen Bierbrauer; Antonio Cossidente; Yves Edel
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 120 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
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 P G(3r -1, q) into a (2r -1)-space, an (r -1)-space and q r -1 cyclic caps, each of size (q 2r -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.
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