  The intersection of a complex plane curve with a small three-sphere
surrounding one of its singularities is a non-trivial link. The refined
punctual Hilbert schemes of the singularity parameterize subschemes supported
at the singular point of fixed length and whose defining ideals have a fixed
number of generators. We conjecture that the generating function of Euler
characteristics of refined punctual Hilbert schemes is the HOMFLY polynomial of
the link. The conjecture is verified for irreducible singularities y^k = x^n,
whose links are the k,n torus knots, and for the singularity y^4 = x^7 - x^6 +
4 x^5 y + 2 x^3 y^2, whose link is the 2,13 cable of the trefoil.
