---
_id: '14244'
abstract:
- lang: eng
  text: "In this paper, we determine the motivic class — in particular, the weight
    polynomial and conjecturally the Poincaré polynomial — of the open de Rham space,
    defined and studied by Boalch, of certain moduli spaces of irregular meromorphic
    connections on the trivial rank \r\n bundle on P1. The computation is by motivic
    Fourier transform. We show that the result satisfies the purity conjecture, that
    is, it agrees with the pure part of the conjectured mixed Hodge polynomial of
    the corresponding wild character variety. We also identify the open de Rham spaces
    with quiver varieties with multiplicities of Yamakawa and Geiss–Leclerc–Schröer.
    We finish with constructing natural complete hyperkähler metrics on them, which
    in the four-dimensional cases are expected to be of type ALF."
acknowledgement: We would like to thank Gergely Bérczy, Roger Bielawski, Philip Boalch,
  Sergey Cherkis, Andrew Dancer, Brent Doran, Eloïse Hamilton, Frances Kirwan, Bernard
  Leclerc, Emmanuel Letellier, Alessia Mandini, Maxence Mayrand, András Némethi, Szilárd
  Szabó, and Daisuke Yamakawa for discussions related to the paper. We especially
  thank the referee for an extensive list of very careful comments. At various stages
  of this project, the authors were supported by the Advanced Grant “Arithmetic and
  physics of Higgs moduli spaces” no. 320593 of the European Research Council, by
  grant no. 153627 and NCCR SwissMAP, both funded by the Swiss National Science Foundation
  as well as by EPF Lausanne and IST Austria. In the final stages of this project,
  MLW was supported by SFB/TR 45 “Periods, moduli and arithmetic of algebraic varieties,”
  subproject M08-10 “Moduli of vector bundles on higher-dimensional varieties.” DW
  was also supported by the Fondation Sciences Mathématiques de Paris, as well as
  public grants overseen by the Agence national de la recherche (ANR) of France as
  part of the Investissements d'avenir program, under reference numbers ANR-10-LABX-0098
  and ANR-15-CE40-0008 (Défigéo).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Tamás
  full_name: Hausel, Tamás
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
- first_name: Michael Lennox
  full_name: Wong, Michael Lennox
  last_name: Wong
- first_name: Dimitri
  full_name: Wyss, Dimitri
  last_name: Wyss
citation:
  ama: Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces.
    <i>Proceedings of the London Mathematical Society</i>. 2023;127(4):958-1027. doi:<a
    href="https://doi.org/10.1112/plms.12555">10.1112/plms.12555</a>
  apa: Hausel, T., Wong, M. L., &#38; Wyss, D. (2023). Arithmetic and metric aspects
    of open de Rham spaces. <i>Proceedings of the London Mathematical Society</i>.
    Wiley. <a href="https://doi.org/10.1112/plms.12555">https://doi.org/10.1112/plms.12555</a>
  chicago: Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric
    Aspects of Open de Rham Spaces.” <i>Proceedings of the London Mathematical Society</i>.
    Wiley, 2023. <a href="https://doi.org/10.1112/plms.12555">https://doi.org/10.1112/plms.12555</a>.
  ieee: T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open
    de Rham spaces,” <i>Proceedings of the London Mathematical Society</i>, vol. 127,
    no. 4. Wiley, pp. 958–1027, 2023.
  ista: Hausel T, Wong ML, Wyss D. 2023. Arithmetic and metric aspects of open de
    Rham spaces. Proceedings of the London Mathematical Society. 127(4), 958–1027.
  mla: Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.”
    <i>Proceedings of the London Mathematical Society</i>, vol. 127, no. 4, Wiley,
    2023, pp. 958–1027, doi:<a href="https://doi.org/10.1112/plms.12555">10.1112/plms.12555</a>.
  short: T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society
    127 (2023) 958–1027.
date_created: 2023-08-27T22:01:18Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:56:10Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/plms.12555
ec_funded: 1
external_id:
  arxiv:
  - '1807.04057'
  isi:
  - '001049312700001'
file:
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  creator: dernst
  date_created: 2024-01-30T12:56:00Z
  date_updated: 2024-01-30T12:56:00Z
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has_accepted_license: '1'
intvolume: '       127'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 958-1027
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '320593'
  name: Arithmetic and physics of Higgs moduli spaces
- _id: 25E6C798-B435-11E9-9278-68D0E5697425
  grant_number: '153627'
  name: Arithmetic quantization of character and quiver varities
publication: Proceedings of the London Mathematical Society
publication_identifier:
  eissn:
  - 1460-244X
  issn:
  - 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic and metric aspects of open de Rham spaces
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 127
year: '2023'
...