Non-algebraicity of Deligne--Hitchin twistor spaces

Abstract

In this paper, we prove that on a smooth complex projective curve of positive genus, the Deligne--Hitchin twistor spaces for the structure groups GL(n,ℂ) (n≥1) and SL(n,ℂ) (n≥2) admit no algebraization by a complex scheme locally of finite type. When the genus is at least two, the same holds for their stable loci and hence for the corresponding Hitchin twistor spaces. Nevertheless, the Deligne--Hitchin twistor spaces admit ℝ_alg-definable complex analytic structures when the rank or the genus is one.

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BibTeX RIS

BibTeX

@misc{huang2026nonalgebraicity,
  title = {{Non-algebraicity of Deligne--Hitchin twistor spaces}},
  author = {Pengfei Huang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27699},
  eprint = {2609.27699},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27699},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Non-algebraicity of Deligne--Hitchin twistor spaces
AU  - Pengfei Huang
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.27699
UR  - https://arxiv.org/abs/2609.27699
AB  - In this paper, we prove that on a smooth complex projective curve of positive genus, the Deligne--Hitchin twistor spaces for the structure groups GL(n,ℂ) (n≥1) and SL(n,ℂ) (n≥2) admit no algebraization by a complex scheme locally of finite type. When the genus is at least two, the same holds for their stable loci and hence for the corresponding Hitchin twistor spaces. Nevertheless, the Deligne--Hitchin twistor spaces admit ℝ_alg-definable complex analytic structures when the rank or the genus is one.
ER  -

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