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arXiv · 2606.20938

The Parity of Invariant Characteristics

Linden Disney-Hogg
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Abstract

We demonstrate a method to prove that a theta characteristic on Riemann surface $S$ invariant under the action of $G \leq \mathrm{Aut}(S)$ has even parity by considering the representation theory of the double cover $\tilde{G} = 2 \cdot G$. We apply this to certain Hurwitz curves, and prove a recent conjecture of Broughton \& Disney-Hogg.

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Linden Disney-Hogg. 2026-06-18. The Parity of Invariant Characteristics. https://arxiv.org/abs/2606.20938

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