The Cayley–Bacharach property and the Levinson–Ullery conjecture

In this paper, we study the geometric configurations of a finite set of points having the Cayley–Bacharach property in the [Formula: see text]-dimensional projective space [Formula: see text]. Our main contribution is the proof of the Levinson–Ullery conjecture for the previously unsolved case where [Formula: see text] and [Formula: see text].