Let m be a positive integer and q be a prime power. In this paper sets of points of PG(r, q), r ≥ 3, intersected by any hyperplane in m or mq+1 points are studied. Their size is determined and for r even it is proved that such sets are the subspaces of PG(r, q). For r odd, under an extra condition it is proved that r = 3 and that such a set is either a line or an ovoid.
On sets of points of PG(r,q), r ≥ 3, of hyperplane-type (m; mq + 1)r-1
Vito Napolitano
In corso di stampa
Abstract
Let m be a positive integer and q be a prime power. In this paper sets of points of PG(r, q), r ≥ 3, intersected by any hyperplane in m or mq+1 points are studied. Their size is determined and for r even it is proved that such sets are the subspaces of PG(r, q). For r odd, under an extra condition it is proved that r = 3 and that such a set is either a line or an ovoid.File in questo prodotto:
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