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Stratification of Joint Moduli Spaces of Higgs Bundles

  • Shiyu Cao
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Abstract

We study the marked analytic moduli space of polystable degree-zero SLr(C)-Higgs bundles over Teichmüller space. The connected components of the orbit-type loci defined by the full determinant-one stabilizers form a complex Whitney stratification. The projection to Teichmüller space is a holomorphic submersion on every stratum. Each stratum carries a canonical relative holomorphic symplectic form. These forms determine a vertical holomorphic Poisson bracket on the reduced structure sheaf, whose symplectic leaves are the connected orbit-type strata in the fibers. On each fiber, the Hitchin--Kobayashi correspondence is biholomorphic on every stratum and identifies its hyperkähler structure. The harmonic representatives and vertical hyperkähler tensors vary smoothly along the strata of the total space.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026stratification,
  title = {{Stratification of Joint Moduli Spaces of Higgs Bundles}},
  author = {Shiyu Cao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00378},
  eprint = {2610.00378},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00378},
}
RIS
TY  - UNPB
TI  - Stratification of Joint Moduli Spaces of Higgs Bundles
AU  - Shiyu Cao
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00378
UR  - https://arxiv.org/abs/2610.00378
AB  - We study the marked analytic moduli space of polystable degree-zero SL_r(C)-Higgs bundles over Teichmüller space. The connected components of the orbit-type loci defined by the full determinant-one stabilizers form a complex Whitney stratification. The projection to Teichmüller space is a holomorphic submersion on every stratum. Each stratum carries a canonical relative holomorphic symplectic form. These forms determine a vertical holomorphic Poisson bracket on the reduced structure sheaf, whose symplectic leaves are the connected orbit-type strata in the fibers. On each fiber, the Hitchin--Kobayashi correspondence is biholomorphic on every stratum and identifies its hyperkähler structure. The harmonic representatives and vertical hyperkähler tensors vary smoothly along the strata of the total space.
ER  -