The Cayley-Bacharach Property and The Levinson-Ullery Conjecture

Key Points

• The aim is to explore the Cayley-Bacharach property for points in projective space and prove the Levinson-Ullery conjecture in a specific case.
• Analyzed geometric configurations of finite sets of points in projective space.
• Utilized geometric properties related to the Cayley-Bacharach property.
• Focused on a case where specific dimensions are set.
• Successfully proved the Levinson-Ullery conjecture for the unsolved case with specific dimensions.
• Demonstrated new relationships between point configurations and the Cayley-Bacharach property.