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PreprintCC BY 4.0arXiv

Finiteness of open substacks with proper moduli spaces

  • Xucheng Zhang
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Abstract

For an algebraic stack of finite type, we construct a finite stratification of an atlas such that every universally closed open substack pulls back to a union of strata. As a result, there are only finitely many open substacks admitting a proper adequate moduli space.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026finiteness,
  title = {{Finiteness of open substacks with proper moduli spaces}},
  author = {Xucheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16706},
  eprint = {2610.16706},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16706},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finiteness of open substacks with proper moduli spaces
AU  - Xucheng Zhang
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16706
UR  - https://arxiv.org/abs/2610.16706
AB  - For an algebraic stack of finite type, we construct a finite stratification of an atlas such that every universally closed open substack pulls back to a union of strata. As a result, there are only finitely many open substacks admitting a proper adequate moduli space.
ER  -