  Let S be a smooth projective surfaces and S^[n] the Hilbert scheme of
zero-dimensional subschemes of S of length n. We proof that the class of S^[n]
in the complex cobordism ring depends only on the class of the surface itself.
Moreover, we compute the cohomology and holomorphic Euler characterisitcs of
certain tautological sheaves on S^[n] and prove results on the general
structure of certain integrals over polynomials in Chern classes of
tautological sheaves.
