Caps on Classical Varieties and their Projections

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Department of Mathematical Sciences


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