The homotopy type of spaces of coprime polynomials revisited

The purpose of this paper is to study the topology of certain toric varieties XIXI, arising as quotients of the action of C⁎C⁎ on complements of arrangements of coordinate subspaces in CnCn, and to improve the homotopy stability dimension for the inclusion map id:Hold⁎(S2,XI)→Mapd⁎(S2,XI) given in [11] by making use of the Vassiliev spectral sequence.We also improve the homotopy stability dimension of this inclusion given by G. Segal [18] for XI=CPn−1XI=CPn−1 and n≥3n≥3.