Towards a Combinatorial Description of the Intersection Product on ${\mathbb{P}}^{2[N]}$

Abstract

We prove that there is an algorithm to compute the class of the intersection of the divisor of schemes incident to a fixed line with any other class of a basis of the Chow ring $A^{\ast }({\mathbb{P}}^{2[N]})$ due to Mallavibarrena and Sols. This is progress towards a combinatorial description of the intersection product on the Hilbert scheme of points in the projective plane.