[{"month":"02","article_number":"2202.10909","_id":"10788","date_created":"2022-02-23T09:04:43Z","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."}],"date_published":"2022-02-22T00:00:00Z","arxiv":1,"article_processing_charge":"No","publication":"arXiv","department":[{"_id":"TiBr"}],"status":"public","publication_status":"submitted","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2202.10909"}],"day":"22","author":[{"full_name":"Wilsch, Florian Alexander","first_name":"Florian Alexander","last_name":"Wilsch","orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"type":"preprint","year":"2022","oa_version":"Preprint","citation":{"ieee":"F. A. Wilsch, “Integral points of bounded height on a certain toric variety,” <i>arXiv</i>. .","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>.","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>.","short":"F.A. Wilsch, ArXiv (n.d.).","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>"},"title":"Integral points of bounded height on a certain toric variety","external_id":{"arxiv":["2202.10909"]},"keyword":["Integral point","toric variety","Manin's conjecture"],"language":[{"iso":"eng"}],"date_updated":"2023-05-03T07:46:35Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.48550/arXiv.2202.10909","project":[{"grant_number":"P32428","name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"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."},{"project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"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.","doi":"10.1017/S1474748022000482","keyword":["Integral points","del Pezzo surface","universal torsor","Manin’s conjecture"],"language":[{"iso":"eng"}],"title":"Integral points on singular del Pezzo surfaces","citation":{"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, 2022. <a href=\"https://doi.org/10.1017/S1474748022000482\">https://doi.org/10.1017/S1474748022000482</a>.","ista":"Derenthal U, Wilsch FA. 2022. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu.","ieee":"U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2022.","mla":"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, 2022, doi:<a href=\"https://doi.org/10.1017/S1474748022000482\">10.1017/S1474748022000482</a>.","short":"U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu (2022).","ama":"Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2022. doi:<a href=\"https://doi.org/10.1017/S1474748022000482\">10.1017/S1474748022000482</a>","apa":"Derenthal, U., &#38; Wilsch, F. A. (2022). 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>"},"type":"journal_article","author":[{"first_name":"Ulrich","full_name":"Derenthal, Ulrich","last_name":"Derenthal"},{"orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander"}],"day":"10","isi":1,"publisher":"Cambridge University Press","status":"public","publication":"Journal of the Institute of Mathematics of Jussieu","department":[{"_id":"TiBr"}],"quality_controlled":"1","date_created":"2021-09-15T10:06:48Z","month":"11","publication_identifier":{"eissn":["1475-3030 "],"issn":["1474-7480"]},"external_id":{"isi":["000881319200001"],"arxiv":["2109.06778"]},"scopus_import":"1","date_updated":"2023-08-02T06:55:10Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2022","oa_version":"Published Version","article_type":"original","oa":1,"main_file_link":[{"url":"https://doi.org/10.1017/S1474748022000482","open_access":"1"}],"publication_status":"epub_ahead","article_processing_charge":"Yes (via OA deal)","arxiv":1,"_id":"10018","date_published":"2022-11-10T00:00:00Z","abstract":[{"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.","lang":"eng"}]}]