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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

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✦ 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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