Cayley–Bacharach theorem
= Cayley–Bacharach theorem
{wiki=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 \\).