Spaces of holomorphic maps with bounded multiplicity

Let Hol(d)*(S-2, CPn-1) be the space consisting of all basepoint preserving holomorphic maps f : S-2 --> CPn-1 of degree d. Then it is homeomorphic to the n-tuples (P-1( z),..., Pn (z)) epsilon C[z](n) Of monic polynomials of degree d with no common root. Segal proved that it is a finite-dimensional model of Omega (CPn-1)-C-2. In this paper, we consider a certain subspace of it defined using the concept of multiplicity of roots, and we prove that it is also a finite-dimensional model of certain double loop space.