发表机构
Chern Institute of Mathematics, Nankai University（南开大学陈省身数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用解析方法构造了带标记的多重稳定 $\mathrm{SL}_r(\mathbb C)$-Higgs 丛的模空间，证明其正规、Hausdorff，局部为 Teichmüller 邻域与二次锥商的乘积，并验证了与已知模空间的一致性。
AI 中文摘要
我们通过解析方法构造了带标记的多重稳定 $\mathrm{SL}_r(\mathbb C)$-Higgs 丛的模空间。所得空间是正规且 Hausdorff 的，其局部模型是 Teichmüller 邻域与二次锥的商空间的乘积。这些模型保留了曲线参数并识别了稳定化子。我们证明了该空间与复和酉规范商拓扑的一致性，并确立了在约化解析基上的半稳定族的粗模性质。映射类群和 Higgs 缩放作用是全纯的。此外，在稳定轨迹上，我们所考虑的模空间与 Collier、Toulisse 和 Wentworth 构造的联合模空间一致。
英文摘要
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 parameter and identify the stabilizers. We prove agreement with the complex and unitary gauge-quotient topologies and establish the coarse moduli property for semistable families over reduced analytic bases. The mapping class group and Higgs scaling act holomorphically. Besides, on the stable locus, the moduli spaces that we consider agree with the joint moduli constructed by Collier, Toulisse and Wentworth.
