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PreprintCC BY 4.0arXiv

Intrinsic Non-Reductive Geometric Invariant Theory and Moduli Spaces of Principal Bundles with Non-Reductive Structure Groups

  • George Cooper
  • Ludvig Modin
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Abstract

We prove the existence of moduli spaces for algebraic stacks with a weak action of Θ= [𝔸1/𝔾m] (including stacks of filtered objects and unstable Θ-strata) for which the center admits a good moduli space and the retraction to the center has flat, finitely presented relative inertia, providing a stack-intrinsic generalization of the existence of non-reductive Geometric Invariant Theory quotients. As an application, we construct quasi-projective coarse moduli spaces of principal bundles over a smooth projective curve with non-reductive structure groups, including moduli spaces of Ramanathan unstable principal bundles of fixed Harder--Narasimhan type.

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Cite

BibTeXRIS
BibTeX
@misc{cooper2026intrinsic,
  title = {{Intrinsic Non-Reductive Geometric Invariant Theory and Moduli Spaces of Principal Bundles with Non-Reductive Structure Groups}},
  author = {George Cooper and Ludvig Modin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38837},
  eprint = {2610.38837},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38837},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Intrinsic Non-Reductive Geometric Invariant Theory and Moduli Spaces of Principal Bundles with Non-Reductive Structure Groups
AU  - George Cooper
AU  - Ludvig Modin
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38837
UR  - https://arxiv.org/abs/2610.38837
AB  - We prove the existence of moduli spaces for algebraic stacks with a weak action of Θ= [𝔸^1/𝔾_m] (including stacks of filtered objects and unstable Θ-strata) for which the center admits a good moduli space and the retraction to the center has flat, finitely presented relative inertia, providing a stack-intrinsic generalization of the existence of non-reductive Geometric Invariant Theory quotients. As an application, we construct quasi-projective coarse moduli spaces of principal bundles over a smooth projective curve with non-reductive structure groups, including moduli spaces of Ramanathan unstable principal bundles of fixed Harder--Narasimhan type.
ER  -