On the Geometry of Hermitian Matrices of Order Three Over Finite Fields

Authors: Cossidente A.1; Siciliano A.2

Source: European Journal of Combinatorics, Volume 22, Number 8, November 2001 , pp. 1047-1058(12)

Publisher: Academic Press

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Abstract:

Some geometry of Hermitian matrices of order three over GF(q2) is studied. The variety coming from rank 2 matrices is a cubic hypersurface M73of PG(8,q) whose singular points form a variety H corresponding to all rank 1 Hermitian matrices. BesideM73turns out to be the secant variety of H. We also define the Hermitian embedding of the point-set of PG(2, q2) whose image is exactly the variety H. It is a cap and it is proved that PGL(3, q2) is a subgroup of all linear automorphisms of H. Further, the Hermitian lifting of a collineation of PG(2, q2) is defined. By looking at the point orbits of such lifting of a Singer cycle of PG(2, q2) new mixed partitions of PG(8,q) into caps and linear subspaces are given. Copyright 2001 Academic Press

Language: English

Document Type: Research article

Affiliations: 1: Dipartimento di Matematica, Università della Basilicata, Contrada Macchia Romana, 85100 Potenza, Italy 2: Dipartimento di Matematica, Università di Roma “La Sapienza", Piazzale Aldo Moro, 5, 00185 Roma, Italy

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