---
_id: '17437'
abstract:
- lang: eng
  text: We prove that the zero-fiber of the moment map of a totally negative quiver
    has rational singularities. Our proof consists in generalizing dimension bounds
    on jet spaces of this fiber, which were introduced by Budur. We also transfer
    the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau
    categories, based on recent work of Davison. This has interesting arithmetic applications
    on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories.
    First, we generalize results of Wyss on the asymptotic behaviour of counts of
    jets of quiver moment maps over finite fields. Moreover, we interpret the limit
    of counts of jets on a given moduli space as its p-adic volume under a canonical
    measure analogous to the measure built by Carocci, Orecchia and Wyss on certain
    moduli spaces of coherent sheaves.
acknowledgement: "I would like to warmly thank Dimitri Wyss for his guidance and supervision
  and Nero Budur for helpful discussions and answering all my questions on his previous
  works. I would also like to thank Francesca Carocci, Ben Davison, Lucien Hennecart
  and Olivier Schiffmann for helpful remarks and discussions during the writing of
  this paper. Finally, I would like to thank the anonymous referees for their careful
  reading and suggesting improvements in the exposition.\r\nOpen access funding provided
  by Institute of Science and Technology (IST Austria). This work was supported by
  the Swiss National Science Foundation [No. 196960]. This project has also received
  funding from the European Union’s Horizon 2020 research and innovation programme
  under the Marie Skłodowska-Curie Grant Agreement No. 101034413."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Tanguy
  full_name: Vernet, Tanguy
  id: 19f1e3bf-c59a-11ee-a1af-ed269948817b
  last_name: Vernet
citation:
  ama: Vernet T. Rational singularities for moment maps of totally negative quivers.
    <i>Transformation Groups</i>. 2024. doi:<a href="https://doi.org/10.1007/s00031-024-09873-0">10.1007/s00031-024-09873-0</a>
  apa: Vernet, T. (2024). Rational singularities for moment maps of totally negative
    quivers. <i>Transformation Groups</i>. Springer Nature. <a href="https://doi.org/10.1007/s00031-024-09873-0">https://doi.org/10.1007/s00031-024-09873-0</a>
  chicago: Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative
    Quivers.” <i>Transformation Groups</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00031-024-09873-0">https://doi.org/10.1007/s00031-024-09873-0</a>.
  ieee: T. Vernet, “Rational singularities for moment maps of totally negative quivers,”
    <i>Transformation Groups</i>. Springer Nature, 2024.
  ista: Vernet T. 2024. Rational singularities for moment maps of totally negative
    quivers. Transformation Groups.
  mla: Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative
    Quivers.” <i>Transformation Groups</i>, Springer Nature, 2024, doi:<a href="https://doi.org/10.1007/s00031-024-09873-0">10.1007/s00031-024-09873-0</a>.
  short: T. Vernet, Transformation Groups (2024).
corr_author: '1'
date_created: 2024-08-18T22:01:04Z
date_published: 2024-09-09T00:00:00Z
date_updated: 2025-09-08T08:56:08Z
day: '09'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00031-024-09873-0
ec_funded: 1
external_id:
  isi:
  - '001287455300001'
has_accepted_license: '1'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s00031-024-09873-0
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Transformation Groups
publication_identifier:
  eissn:
  - 1531-586X
  issn:
  - 1083-4362
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rational singularities for moment maps of totally negative quivers
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...