  The Jack symmetric polynomials $P_\lambda^{(\alpha)}$ form a class of
symmetric polynomials which are indexed by a partition $\lambda$ and depend
rationally on a parameter $\alpha$. They reduced to the Schur polynomials when
$\alpha=1$, and to other classical families of symmetric polynomials for
several specific parameters.
  It is well-known that Schur polynomials can be realized as certain elements
of homology groups of Grassmann manifolds. The purpose of this paper is to give
a similar geometric realization for Jack polynomials. However, spaces which we
use are totally different. Our spaces are Hilbert schemes of points on a
surface X which is the total space of a line bundle L over the projective line.
The parameter $\alpha$ in Jack polynomials relates to our surface X by $\alpha
= -<C,C>$, where C is the zero section, and <C,C> is the self-intersection
number of C.
