  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.
