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PreprintCC BY 4.0arXiv

Untwisting the twisted character variety via a stacky curve

  • Anna Borri
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Abstract

Given a smooth projective curve X over β„‚, we show that the twisted character variety of X is equivalent to a component of the character variety of a stacky curve 𝒳, constructed by adding an orbifold point to X. This allows to interpret the non abelian Hodge correspondence in degree d over X as a statement about the geometry of the Hodge moduli space of Ξ»-connections on 𝒳. Following Shende's approach (see arXiv:1411.4975), we exploit this interpretation to compute the weights of the tautological classes on the cohomology of the twisted character variety, by replacing 𝒳 with a simplicial scheme Δ𝒳 obtained from a triangulation.

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Cite

BibTeXRIS
BibTeX
@misc{borri2026untwisting,
  title = {{Untwisting the twisted character variety via a stacky curve}},
  author = {Anna Borri},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24584},
  eprint = {2609.24584},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24584},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Untwisting the twisted character variety via a stacky curve
AU  - Anna Borri
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24584
UR  - https://arxiv.org/abs/2609.24584
AB  - Given a smooth projective curve X over β„‚, we show that the twisted character variety of X is equivalent to a component of the character variety of a stacky curve 𝒳, constructed by adding an orbifold point to X. This allows to interpret the non abelian Hodge correspondence in degree d over X as a statement about the geometry of the Hodge moduli space of Ξ»-connections on 𝒳. Following Shende's approach (see arXiv:1411.4975), we exploit this interpretation to compute the weights of the tautological classes on the cohomology of the twisted character variety, by replacing 𝒳 with a simplicial scheme Ξ”_𝒳 obtained from a triangulation.
ER  -