The Cayley-Bacharach property and the Levinson-Ullery conjecture

TL;DR

This paper proves the Levinson-Ullery conjecture for a specific case involving finite point sets with the Cayley-Bacharach property in projective spaces, advancing understanding of geometric configurations.

Contribution

It provides a proof of the Levinson-Ullery conjecture for the case where d=4 and r≥1, which was previously unresolved.

Findings

Confirmed the conjecture for d=4, r≥1

Enhanced understanding of Cayley-Bacharach configurations

Extended geometric theory in projective spaces

Abstract

In this paper, we study the geometric configurations of a finite set of points having the Cayley-Bacharach property in the $n$-dimensional projective space $\bbP^n$. Our main contribution is the proof of the Levinson-Ullery conjecture for the previously unsolved case where $d=4$ and $r\ge 1$.