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Proves the Levinson-Ullery conjecture regarding geometric configurations in projective space, indicating new insights in higher dimensions.
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] 4.
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Lê et al. (2026) studied this question.
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