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An analytic construction of the universal moduli space of SLr(ℂ)-Higgs bundles

  • Shiyu Cao
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Abstract

We construct the moduli space of marked polystable SLr(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.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026analytic,
  title = {{An analytic construction of the universal moduli space of $\mathrmSL_r(\mathbb C)$-Higgs bundles}},
  author = {Shiyu Cao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25807},
  eprint = {2609.25807},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25807},
}
RIS
TY  - UNPB
TI  - An analytic construction of the universal moduli space of SL_r(ℂ)-Higgs bundles
AU  - Shiyu Cao
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.25807
UR  - https://arxiv.org/abs/2609.25807
AB  - We construct the moduli space of marked polystable SL_r(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.
ER  -