An intersection number for the punctual Hilbert scheme of a surface
  Let 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. 
Geir Ellingsrud and Stein Arild Str{\o}mme