In  Stefano Innamorati and Mauro Zannetti gave a characterization of the planes secant to a non-singular quadric in PG(4, q). Their result is based on a particular hypothesis (we call it “polynomial”) that, as the same authors wrote at the end of the paper, could not exclude possible sporadic cases. In this paper we improve their result by giving a characterization without the “polynomial” hypothesis. So possible sporadic cases are definitely excluded.
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