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A note on a characterization of a quadric cone

Abstract In a paper of 2002 Stefania Ferri gave a characterization of a quadric cone in PG(3, q). The statement of the theorem is true, but the first part of the proof does not work. The same author in a paper of 2004 gave a new correct, but quite tedious, proof of that part. In this short note we prove the first part in a simpler way.