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The variety of (n + 1) × (n + 1) rank one Hermitian matrices over a finite field F 2 q , which is naturally in one-to-one correspondence with the points of a projective space PG(n, q 2) and which gives rise to a cap in the projective space PG(n 2 +2n, q) on which the group PGL(n + 1, q 2) acts 2-transitively is studied. Our main result is a geometric characterization of this cap and some of its projections along the lines of the characterization of quadric Veroneseans by Mazzocca and Melone.

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