[{"day":"10","title":"Integral points on singular del Pezzo surfaces","researchdata_availability":"no","publication":"Journal of the Institute of Mathematics of Jussieu","corr_author":"1","page":"1259-1294","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"eissn":["1475-3030 "],"issn":["1474-7480"]},"scopus_import":"1","isi":1,"oa":1,"date_published":"2024-05-10T00:00:00Z","fulldoi":"https://doi.org/10.1017/S1474748022000482","arxiv":1,"year":"2024","_id":"10018","oa_version":"Published Version","article_type":"original","keyword":["Integral points","del Pezzo surface","universal torsor","Manin’s conjecture"],"type":"journal_article","file":[{"success":1,"date_created":"2024-06-03T08:33:29Z","relation":"main_file","file_name":"2024_JourMathJussieu_Derenthal.pdf","file_id":"17102","date_updated":"2024-06-03T08:33:29Z","content_type":"application/pdf","checksum":"c4698ea12cfe10ef2c6c79880290c7ac","access_level":"open_access","creator":"dernst","file_size":592305}],"volume":23,"acknowledgement":"The first author was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.","language":[{"iso":"eng"}],"date_created":"2021-09-15T10:06:48Z","das_tickbox":"0","status":"public","quality_controlled":"1","external_id":{"arxiv":["2109.06778"],"isi":["000881319200001"]},"supplementarymaterial":"no","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture","call_identifier":"FWF"}],"month":"05","publication_status":"published","date_updated":"2026-07-29T10:00:51Z","issue":"3","abstract":[{"lang":"eng","text":"In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines."}],"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2024-06-03T08:33:29Z","department":[{"_id":"TiBr"}],"publisher":"Cambridge University Press","has_accepted_license":"1","author":[{"first_name":"Ulrich","full_name":"Derenthal, Ulrich","last_name":"Derenthal"},{"last_name":"Wilsch","orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander"}],"doi":"10.1017/S1474748022000482","intvolume":"        23","citation":{"ieee":"U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 3. Cambridge University Press, pp. 1259–1294, 2024.","ama":"Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2024;23(3):1259-1294. doi:<a href=\"https://doi.org/10.1017/S1474748022000482\">10.1017/S1474748022000482</a>","apa":"Derenthal, U., &#38; Wilsch, F. A. (2024). Integral points on singular del Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S1474748022000482\">https://doi.org/10.1017/S1474748022000482</a>","chicago":"Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/S1474748022000482\">https://doi.org/10.1017/S1474748022000482</a>.","mla":"Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 3, Cambridge University Press, 2024, pp. 1259–94, doi:<a href=\"https://doi.org/10.1017/S1474748022000482\">10.1017/S1474748022000482</a>.","ista":"Derenthal U, Wilsch FA. 2024. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. 23(3), 1259–1294.","short":"U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu 23 (2024) 1259–1294."},"ddc":["510"]},{"department":[{"_id":"TiBr"}],"main_file_link":[{"url":"https://arxiv.org/abs/2202.10909","open_access":"1"}],"abstract":[{"lang":"eng","text":"We determine an asymptotic formula for the number of integral points of\r\nbounded height on a certain toric variety, which is incompatible with part of a\r\npreprint by Chambert-Loir and Tschinkel. We provide an alternative\r\ninterpretation of the asymptotic formula we get. To do so, we construct an\r\nanalogue of Peyre's constant $\\alpha$ and describe its relation to a new\r\nobstruction to the Zariski density of integral points in certain regions of\r\nvarieties."}],"article_processing_charge":"No","citation":{"short":"F.A. Wilsch, ArXiv (n.d.).","ista":"Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.","chicago":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2202.10909\">https://doi.org/10.48550/arXiv.2202.10909</a>.","apa":"Wilsch, F. A. (n.d.). Integral points of bounded height on a certain toric variety. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2202.10909\">https://doi.org/10.48550/arXiv.2202.10909</a>","ama":"Wilsch FA. Integral points of bounded height on a certain toric variety. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2202.10909\">10.48550/arXiv.2202.10909</a>","ieee":"F. A. Wilsch, “Integral points of bounded height on a certain toric variety,” <i>arXiv</i>. .","mla":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain Toric Variety.” <i>ArXiv</i>, 2202.10909, doi:<a href=\"https://doi.org/10.48550/arXiv.2202.10909\">10.48550/arXiv.2202.10909</a>."},"doi":"10.48550/arXiv.2202.10909","author":[{"id":"560601DA-8D36-11E9-A136-7AC1E5697425","orcid":"0000-0001-7302-8256","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","first_name":"Florian Alexander"}],"external_id":{"arxiv":["2202.10909"]},"supplementarymaterial":"no","status":"public","date_created":"2022-02-23T09:04:43Z","das_tickbox":"0","date_updated":"2026-08-06T10:31:31Z","publication_status":"submitted","month":"02","project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"keyword":["Integral point","toric variety","Manin's conjecture"],"arxiv":1,"year":"2022","_id":"10788","oa_version":"Preprint","language":[{"iso":"eng"}],"acknowledgement":"Part of this work was conducted as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.\r\nDuring this time, I had interesting and fruitful discussions on the interpretation of the result for\r\nthe toric variety discussed in Section 3 with Antoine Chambert-Loir. I wish to thank him for these\r\nopportunities and for his useful remarks on earlier versions of this article. This work was partly\r\nfunded by FWF grant P 32428-N35.","type":"preprint","researchdata_availability":"no","publication":"arXiv","title":"Integral points of bounded height on a certain toric variety","article_number":"2202.10909","day":"22","date_published":"2022-02-22T00:00:00Z","fulldoi":"https://doi.org/10.48550/arXiv.2202.10909","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1"}]