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Asymptotics of the Moduli Spaces of Parabolic SL(3,ℂ)-Higgs Bundles

  • Shiyu Cao
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Abstract

We study the large-scale geometry of the moduli spaces of stable strongly parabolic SL(3,C)-Higgs bundles on the three-punctured sphere for a family of parabolic weights. We glue the local Toda model metric to a decoupled metric obtained from the spectral line bundle, and perturb the resulting approximate metrics to harmonic metrics adapted to the parabolic structure. We also prove that Hitchin's L2 metric approaches the semi-flat metric exponentially. The metric comparison and the spectral period calculation show that each moduli space is a complete ALG gravitational instanton of type E6. The asymptotic estimates are uniform on compact subintervals of the weight chamber.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026asymptotics,
  title = {{Asymptotics of the Moduli Spaces of Parabolic $\mathrmSL(3,\mathbb C)$-Higgs Bundles}},
  author = {Shiyu Cao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21303},
  eprint = {2610.21303},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21303},
}
RIS
TY  - UNPB
TI  - Asymptotics of the Moduli Spaces of Parabolic SL(3,ℂ)-Higgs Bundles
AU  - Shiyu Cao
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21303
UR  - https://arxiv.org/abs/2610.21303
AB  - We study the large-scale geometry of the moduli spaces of stable strongly parabolic SL(3,C)-Higgs bundles on the three-punctured sphere for a family of parabolic weights. We glue the local Toda model metric to a decoupled metric obtained from the spectral line bundle, and perturb the resulting approximate metrics to harmonic metrics adapted to the parabolic structure. We also prove that Hitchin's L^2 metric approaches the semi-flat metric exponentially. The metric comparison and the spectral period calculation show that each moduli space is a complete ALG gravitational instanton of type E_6. The asymptotic estimates are uniform on compact subintervals of the weight chamber.
ER  -