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The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings

  • Luca Battistella
  • Andrea Di Lorenzo
  • Michele Pernice
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Abstract

We classify all open substacks admitting a proper good moduli space inside the stack 𝒢1,n of log-canonically polarized Gorenstein curves of genus one with n distinct marked points: they are exactly the stacks ℳ̅1,n(c) defined by Bozlee--Kuo--Neff. Restricting to the case where c is pure of level m, we then give a numerical criterion for the projectivity of the good moduli spaces: these turn out to be asymptotically almost never projective as n tends to infinity.

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Cite

BibTeXRIS
BibTeX
@misc{battistella2026unbearable,
  title = {{The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings}},
  author = {Luca Battistella and Andrea Di Lorenzo and Michele Pernice},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08742},
  eprint = {2610.08742},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08742},
}
RIS
TY  - UNPB
TI  - The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings
AU  - Luca Battistella
AU  - Andrea Di Lorenzo
AU  - Michele Pernice
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08742
UR  - https://arxiv.org/abs/2610.08742
AB  - We classify all open substacks admitting a proper good moduli space inside the stack 𝒢_1,n of log-canonically polarized Gorenstein curves of genus one with n distinct marked points: they are exactly the stacks ℳ̅_1,n(c) defined by Bozlee--Kuo--Neff. Restricting to the case where c is pure of level m, we then give a numerical criterion for the projectivity of the good moduli spaces: these turn out to be asymptotically almost never projective as n tends to infinity.
ER  -