2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150124Let S be a smooth projective surface, and consider the following two subvarieties of the Hilbert scheme parameterizing closed subschemes of S of length n: A = {subschemes with support in a fixed point of S} B = {subschemes with support in one (variable) point of S} A and B have complementary dimensions in the Hilbert scheme. We prove that the intersection number [A].[B] = n(-1)^(n-1), answering a question by H. Nakajima.AMSLaTeX v 1.2, 7 pagesAlgebraic Geometry14C17, 14C05text