Multi-homogeneous Bézout theorem

The Multi-homogeneous Bézout theorem is an extension of Bézout's theorem to the setting of multi-homogeneous polynomials. It concerns the intersection of varieties defined by such polynomials. ### Background Bézout's theorem states that the number of intersection points of two projective varieties in projective space is equal to the product of their degrees, provided that the varieties intersect transversely and we consider appropriate multiplicities.