An upper bound on the topological complexity of discriminantal varieties

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.

Keywords

topological complexity, configuration space, affine variety, equivariant topological complexity

2010 Mathematics Subject Classification

14L30, 55M30, 55R80

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The author was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2047/1, 390685813), and by the Danish National Research Foundation through the Centre for Geometry and Topology (DNRF151) and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 772960).

Received 9 March 2021

Accepted 3 April 2021

Published 6 April 2022