The homotopy type of spaces of coprime polynomials revisited

TL;DR

This paper investigates the topology of specific toric varieties related to coprime polynomials and improves the understanding of homotopy stability dimensions for certain inclusion maps using spectral sequences.

Contribution

It provides new insights into the homotopy stability of spaces of coprime polynomials by employing spectral sequences from simplicial resolutions.

Findings

Improved the homotopy stability dimension for the inclusion map

Analyzed the topology of toric varieties arising from coordinate subspace arrangements

Utilized spectral sequences to enhance previous results

Abstract

The purpose of this paper is to study the topology of certain toric varieties $X_I$, arising as quotients of the action of $\C^*$ on complements of arrangements of coordinate subspaces in $\C^n$, 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.