Mixed Partitions of Projective Geometries |
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Authors: | Arrigo Bonisoli Antonio Cossidente |
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Institution: | (1) Dipartimento di Matematica, Università della Basilicata, via N. Sauro 85, 85100 Potenza, (Italy) |
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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 (qn–1)/(q–1) or (qn–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
of PG(8,q) into caps of size q2+q+1 which are Veronese surfaces. |
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Keywords: | cap Singer cycle mixed partition Kronecker product Veronese surface |
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