{"date_updated":"2024-01-30T12:56:10Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"10","article_processing_charge":"Yes (via OA deal)","day":"01","type":"journal_article","file":[{"checksum":"2af4d2d6a8ae42f7d3fba0188e79ae82","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","file_name":"2023_ProcLondonMathSoc_Hausel.pdf","date_updated":"2024-01-30T12:56:00Z","success":1,"file_id":"14910","date_created":"2024-01-30T12:56:00Z","file_size":651335}],"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."}],"department":[{"_id":"TaHa"}],"issue":"4","publication_status":"published","date_published":"2023-10-01T00:00:00Z","scopus_import":"1","publisher":"Wiley","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-08-27T22:01:18Z","oa_version":"Published Version","oa":1,"status":"public","quality_controlled":"1","title":"Arithmetic and metric aspects of open de Rham spaces","publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"external_id":{"isi":["001049312700001"],"arxiv":["1807.04057"]},"has_accepted_license":"1","author":[{"full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel","first_name":"Tamás"},{"first_name":"Michael Lennox","last_name":"Wong","full_name":"Wong, Michael Lennox"},{"first_name":"Dimitri","last_name":"Wyss","full_name":"Wyss, Dimitri"}],"publication":"Proceedings of the London Mathematical Society","page":"958-1027","doi":"10.1112/plms.12555","_id":"14244","language":[{"iso":"eng"}],"article_type":"original","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>.","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.","short":"T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society 127 (2023) 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>.","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."},"ec_funded":1,"year":"2023","volume":127,"intvolume":"       127","project":[{"call_identifier":"FP7","grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425"},{"grant_number":"153627","name":"Arithmetic quantization of character and quiver varities","_id":"25E6C798-B435-11E9-9278-68D0E5697425"}],"ddc":["510"],"file_date_updated":"2024-01-30T12:56:00Z","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).","isi":1}