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PreprintCC BY 4.0arXiv

Open substacks preserving moduli spaces: classification and bounds

  • Jianping Wang
  • Xucheng Zhang
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Abstract

For a smooth locally reductive stack admitting an adequate moduli space, we show that there are finitely many open substacks preserving the adequate moduli space, and give a complete classification of such opens. For ๐”พm-actions, this becomes an explicit description in terms of the codimension-one Bialynicki-Birula strata. Moreover, for a stable adequate moduli space, we show that the number of preserving opens are bounded by 3 raised to the relative Picard rank. As an application, the number of fixed components for ๐”พm-actions is at least the relative Picard rank.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026open,
  title = {{Open substacks preserving moduli spaces: classification and bounds}},
  author = {Jianping Wang and Xucheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15831},
  eprint = {2610.15831},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15831},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Open substacks preserving moduli spaces: classification and bounds
AU  - Jianping Wang
AU  - Xucheng Zhang
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15831
UR  - https://arxiv.org/abs/2610.15831
AB  - For a smooth locally reductive stack admitting an adequate moduli space, we show that there are finitely many open substacks preserving the adequate moduli space, and give a complete classification of such opens. For ๐”พ_m-actions, this becomes an explicit description in terms of the codimension-one Bialynicki-Birula strata. Moreover, for a stable adequate moduli space, we show that the number of preserving opens are bounded by 3 raised to the relative Picard rank. As an application, the number of fixed components for ๐”พ_m-actions is at least the relative Picard rank.
ER  -