The homotopy type of spaces of coprime polynomials revisited

The purpose of this paper is to study the topology of certain toric varieties $X_I$, arising as quotients of the action of ${\text{C}}^{\ast }$ on complements of arrangements of coordinate subspaces in ${\text{C}}^n$, and to improve the homotopy stability dimension for the inclusion map $i_d:\Hol_d^(S^2,X_I)\to \Map_d^(S^2,X_I)$ given in \cite{GKY1} by using spectral sequences induced from simplicial resolutions.