October 3, 2025Open Access

Representation stability for ordered Hurwitz spaces

Key Points

Representation stability is exhibited in the homology of ordered Hurwitz spaces, providing new insights into their topology.
The study addresses a key question posed by Ellenberg regarding the properties of ordered Hurwitz spaces.
Ordered Hurwitz spaces are moduli spaces characterized by branched covers, reflecting intricate topological behavior.
The findings contribute to the understanding of stability phenomena in complex algebraic structures.

Abstract

In this paper, we study the topology of ordered Hurwitz space. These are moduli spaces of branched covers with a choice of ordering on the branched points. Answering a question of Ellenberg, we prove that the homology of ordered Hurwitz spaces exhibit representation stability.

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Cite This Study

Himes et al. (Fri,) studied this question.

synapsesocial.com/papers/68e034f7f0e39f13e7fa3020 https://doi.org/https://doi.org/10.48550/arxiv.2509.05516

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