An upper bound on the topological complexity of discriminantal varieties

TL;DR

This paper establishes an upper bound on the topological complexity of certain algebraic varieties and applies this to determine the complexity of unordered configuration spaces in the plane.

Contribution

It introduces a new upper bound for the topological complexity of discriminantal varieties and applies it to configuration spaces of the plane.

Findings

Upper bound on topological complexity of discriminantal varieties

Determination of the topological complexity of unordered plane configuration spaces

Provides tools for analyzing the complexity of algebraic varieties

Abstract

We give an upper bound on the topological complexity of varieties $\mathcal{V}$ obtained as complements in $\mathbb{C}^m$ of the zero locus of a polynomial. As an application, we determine the topological complexity of unordered configuration spaces of the plane.