A new characterization of elliptic quadrics in PG(3, q), q odd

Abstract

We prove that a set O of points of PG(3,q), q odd, of line-type (0,m,n)₁, n ≠ q, with a point on which there are at most q+1 lines intersecting O in exactly m points is either an elliptic quadric or n = q + 1 and O is the complement of a line in PG(3,q).