Cayley–Bacharach theorem

The Cayley–Bacharach theorem is a result in algebraic geometry that deals with the intersection of divisors on a projective space. It is particularly relevant in the study of linear systems of divisors and their properties. In its classical form, the theorem states the following: Let \( C \) be a non-singular irreducible curve of degree \( d \) in the projective plane \( \mathbb{P}^2 \).