The Cayley-Bacharach property and the Levinson-Ullery conjecture

2025/11/27 by Le, Ngoc Long, Linh, Tran N. K.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.22113

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 \bbPⁿ. Our main contribution is the proof of the Levinson-Ullery conjecture for the previously unsolved case where d=4 and r≥ 1.

Citations

• The Kähler different of a 0-dimensional scheme
• Geometry of Points Satisfying Cayley-Bacharach Conditions and Applications
• A Cayley-Bacharach theorem and plane configurations
• An application of Liaison theory to zero-dimensional schemes
• On the Cayley-Bacharach Property
• On the Dedekind different of a Cayley-Bacharach scheme

Related

• A Cayley-Bacharach theorem and plane configurations
• An application of Liaison theory to zero-dimensional schemes
• On the Cayley-Bacharach Property
• Geometry of Points Satisfying Cayley-Bacharach Conditions and Applications
• Demailly's Conjecture and the Containment Problem