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PreprintCC BY 4.0arXiv

Simpson filtrations and closure relations of Hodge moduli spaces

  • Zhi Hu
  • Pengfei Huang
  • Fei Yu
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Abstract

In this paper, we study closure relations of Simpson strata in Hodge moduli spaces over a smooth complex projective curve of genus g≥2 and prove in every rank that the Heinloth weight strictly increases whenever a specialization changes the fixed component. For stable full chains, we refine this numerical condition by comparing the degrees of the corresponding filtration steps and construct counterexamples to Simpson's nestedness conjecture for the Dolbeault and de Rham moduli spaces in every rank n≥4. Using the maximum property of this weight, we also discuss Simpson filtrations from the viewpoint of Θ stratifications.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026simpson,
  title = {{Simpson filtrations and closure relations of Hodge moduli spaces}},
  author = {Zhi Hu and Pengfei Huang and Fei Yu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06438},
  eprint = {2610.06438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06438},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Simpson filtrations and closure relations of Hodge moduli spaces
AU  - Zhi Hu
AU  - Pengfei Huang
AU  - Fei Yu
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06438
UR  - https://arxiv.org/abs/2610.06438
AB  - In this paper, we study closure relations of Simpson strata in Hodge moduli spaces over a smooth complex projective curve of genus g≥2 and prove in every rank that the Heinloth weight strictly increases whenever a specialization changes the fixed component. For stable full chains, we refine this numerical condition by comparing the degrees of the corresponding filtration steps and construct counterexamples to Simpson's nestedness conjecture for the Dolbeault and de Rham moduli spaces in every rank n≥4. Using the maximum property of this weight, we also discuss Simpson filtrations from the viewpoint of Θ stratifications.
ER  -