Vandermonde matrices for intersection points of curves

Abstract

We reconsider and reprove Cayley-Bacharach type theorems, as discussed in [1], Theorems CB1-CB5. Our proof naturally uses Max Noether’s famous basis theorem for finitely generated polynomial ideals, but in addition only involves rank properties of Vandermonde matrices. In this way, we even arrive at a slight extension of Theorem CB5. Applications to poised or non-poised problems of multivariate polynomial interpolation are also discussed.