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An analytic construction of the universal moduli space of $\mathrm{SL}_r(\mathbb C)$-Higgs bundles
We construct the moduli space of marked polystable $\mathrm{SL}_r(\mathbb C)$-Higgs bundles via analytic methods. The resulting space is normal and Hausdorff, and its local models are products of a Teichmüller neighbourhood with a quotient of a quadratic cone. These models preserve the curve paramet
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