Starting from a linear collineation of PG(2n-1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n-1,q) consisting of two (n-1)-subspaces and caps, all having size (q^n-1)/(q-1) or (q^n-1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety S_2,2 of PG(8,q) into caps of size q^2+q+1 which are Veronese surfaces.
Mixed Partitions of Projective Geometries / Bonisoli, Arrigo; A., Cossidente. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - STAMPA. - 20:(2000), pp. 143-154. [10.1023/A:1008337524556]
Mixed Partitions of Projective Geometries
BONISOLI, Arrigo;
2000
Abstract
Starting from a linear collineation of PG(2n-1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n-1,q) consisting of two (n-1)-subspaces and caps, all having size (q^n-1)/(q-1) or (q^n-1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety S_2,2 of PG(8,q) into caps of size q^2+q+1 which are Veronese surfaces.Pubblicazioni consigliate
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