Conics and caps |
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Authors: | S. G. Barwick Wen-Ai Jackson Catherine T. Quinn |
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Affiliation: | 1. School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia
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Abstract: | In this article, we begin with arcs in PG(2, q n ) and show that they correspond to caps in PG(2n, q) via the André/Bruck?CBose representation of PG(2, q n ) in PG(2n, q). In particular, we show that a conic of PG(2, q n ) that meets ??? in x points corresponds to a (q n ?+?1 ? x)-cap in PG(2n, q). If x?=?0, this cap is the intersection of n quadrics. If x?=?1 or 2, this cap is contained in the intersection of n quadrics and we discuss ways of extending these caps. We also investigate the structure of the n quadrics. |
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