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PreprintarXiv licencearXiv

Ample stability implies rigidity for quiver moduli

  • Pieter Belmans
  • Gianni Petrella
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Abstract

We show that ample stability suffices to apply Teleman quantisation to the endomorphism bundle of the universal representation on a quiver moduli space, and thus in particular to deduce its infinitesimal rigidity. This answers a question left open in our earlier work with Brecan, Franzen, and Reineke on the sheaf cohomology of universal bundles. This sufficiency makes several recent results applicable in the widest possible range, subject only to ample stability, which for coprime dimension vectors guarantees that the Picard rank of the moduli space is maximal.

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Cite

BibTeXRIS
BibTeX
@misc{belmans2026ample,
  title = {{Ample stability implies rigidity for quiver moduli}},
  author = {Pieter Belmans and Gianni Petrella},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03302},
  eprint = {2610.03302},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03302},
}
RIS
TY  - UNPB
TI  - Ample stability implies rigidity for quiver moduli
AU  - Pieter Belmans
AU  - Gianni Petrella
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03302
UR  - https://arxiv.org/abs/2610.03302
AB  - We show that ample stability suffices to apply Teleman quantisation to the endomorphism bundle of the universal representation on a quiver moduli space, and thus in particular to deduce its infinitesimal rigidity. This answers a question left open in our earlier work with Brecan, Franzen, and Reineke on the sheaf cohomology of universal bundles. This sufficiency makes several recent results applicable in the widest possible range, subject only to ample stability, which for coprime dimension vectors guarantees that the Picard rank of the moduli space is maximal.
ER  -