Spaces of real polynomials with common roots

TL;DR

This paper studies the topological structure of spaces of real polynomials with bounded common roots, providing a stable splitting that enhances understanding of their geometric and algebraic properties.

Contribution

It introduces a stable splitting of the space RX_{k,n}^l, a new topological decomposition for polynomials with limited common roots.

Findings

Stable splitting of RX_{k,n}^l established

Enhanced understanding of polynomial root configurations

Topological properties of polynomial spaces clarified

Abstract

Let RX_{k,n}^l be the space consisting of all (n+1)-tuples (p_0(z),...,p_n(z)) of monic polynomials over R of degree k and such that there are at most l roots common to all p_i(z). In this paper, we prove a stable splitting of RX_{k,n}^l.