{"department":[{"_id":"TiBr"}],"external_id":{"arxiv":["2202.10909"]},"title":"Integral points of bounded height on a certain toric variety","_id":"10788","month":"02","date_updated":"2023-05-03T07:46:35Z","date_created":"2022-02-23T09:04:43Z","keyword":["Integral point","toric variety","Manin's conjecture"],"publication":"arXiv","type":"preprint","day":"22","year":"2022","article_number":"2202.10909","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2202.10909","open_access":"1"}],"project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","grant_number":"P32428"}],"author":[{"first_name":"Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256"}],"date_published":"2022-02-22T00:00:00Z","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.","doi":"10.48550/arXiv.2202.10909","citation":{"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>.","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>. .","ista":"Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.","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>"},"publication_status":"submitted","oa_version":"Preprint","oa":1,"article_processing_charge":"No","language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}