[{"citation":{"mla":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” <i>International Mathematics Research Notices</i>, vol. 2023, no. 8, Oxford Academic, 2023, pp. 6780–808, doi:<a href=\"https://doi.org/10.1093/imrn/rnac048\">10.1093/imrn/rnac048</a>.","ieee":"F. A. Wilsch, “Integral points of bounded height on a log Fano threefold,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 8. Oxford Academic, pp. 6780–6808, 2023.","apa":"Wilsch, F. A. (2023). Integral points of bounded height on a log Fano threefold. <i>International Mathematics Research Notices</i>. Oxford Academic. <a href=\"https://doi.org/10.1093/imrn/rnac048\">https://doi.org/10.1093/imrn/rnac048</a>","ista":"Wilsch FA. 2023. Integral points of bounded height on a log Fano threefold. International Mathematics Research Notices. 2023(8), 6780–6808.","chicago":"Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Log Fano Threefold.” <i>International Mathematics Research Notices</i>. Oxford Academic, 2023. <a href=\"https://doi.org/10.1093/imrn/rnac048\">https://doi.org/10.1093/imrn/rnac048</a>.","ama":"Wilsch FA. Integral points of bounded height on a log Fano threefold. <i>International Mathematics Research Notices</i>. 2023;2023(8):6780-6808. doi:<a href=\"https://doi.org/10.1093/imrn/rnac048\">10.1093/imrn/rnac048</a>","short":"F.A. Wilsch, International Mathematics Research Notices 2023 (2023) 6780–6808."},"intvolume":"      2023","day":"01","abstract":[{"lang":"eng","text":"We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of P3 outside certain planes using universal torsors."}],"status":"public","acknowledgement":"This work was supported by the German Academic Exchange Service. Parts of this article were prepared at the Institut de Mathémathiques de Jussieu—Paris Rive Gauche. I wish to thank Antoine Chambert-Loir for his remarks and the institute for its hospitality, as well as the anonymous referee for several useful remarks and suggestions for improvements.","department":[{"_id":"TiBr"}],"article_type":"original","publication_status":"published","title":"Integral points of bounded height on a log Fano threefold","oa":1,"month":"04","_id":"9034","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/1901.08503","open_access":"1"}],"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"article_processing_charge":"No","isi":1,"volume":2023,"date_updated":"2023-08-01T12:23:55Z","date_created":"2021-01-22T09:31:09Z","year":"2023","quality_controlled":"1","page":"6780-6808","author":[{"last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425","orcid":"0000-0001-7302-8256"}],"publication":"International Mathematics Research Notices","issue":"8","date_published":"2023-04-01T00:00:00Z","oa_version":"Preprint","external_id":{"arxiv":["1901.08503"],"isi":["000773116000001"]},"type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"publisher":"Oxford Academic","doi":"10.1093/imrn/rnac048"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"12","_id":"9199","oa":1,"title":"Equidistribution and freeness on Grassmannians","publication_status":"published","article_type":"original","acknowledgement":"The authors are very grateful to Will Sawin for useful remarks about this topic. While working on this paper the first two authors were supported by EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35.","department":[{"_id":"TiBr"}],"status":"public","abstract":[{"lang":"eng","text":"We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on \"freeness\" for rational points of bounded height on Fano\r\nvarieties."}],"day":"01","citation":{"ieee":"T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness on Grassmannians,” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10. Mathematical Sciences Publishers, pp. 2385–2407, 2022.","mla":"Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10, Mathematical Sciences Publishers, 2022, pp. 2385–407, doi:<a href=\"https://doi.org/10.2140/ant.2022.16.2385\">10.2140/ant.2022.16.2385</a>.","apa":"Browning, T. D., Horesh, T., &#38; Wilsch, F. A. (2022). Equidistribution and freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2022.16.2385\">https://doi.org/10.2140/ant.2022.16.2385</a>","chicago":"Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2022. <a href=\"https://doi.org/10.2140/ant.2022.16.2385\">https://doi.org/10.2140/ant.2022.16.2385</a>.","ista":"Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra &#38; Number Theory. 16(10), 2385–2407.","ama":"Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. 2022;16(10):2385-2407. doi:<a href=\"https://doi.org/10.2140/ant.2022.16.2385\">10.2140/ant.2022.16.2385</a>","short":"T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &#38; Number Theory 16 (2022) 2385–2407."},"intvolume":"        16","doi":"10.2140/ant.2022.16.2385","publisher":"Mathematical Sciences Publishers","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","oa_version":"Preprint","external_id":{"arxiv":["2102.11552"],"isi":["000961514100004"]},"date_published":"2022-12-01T00:00:00Z","publication":"Algebra & Number Theory","issue":"10","author":[{"full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Horesh","first_name":"Tal","full_name":"Horesh, Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425","full_name":"Wilsch, Florian Alexander","first_name":"Florian Alexander","last_name":"Wilsch"}],"quality_controlled":"1","page":"2385-2407","date_created":"2021-02-25T09:56:57Z","year":"2022","date_updated":"2023-08-02T06:46:38Z","project":[{"grant_number":"EP-P026710-2","name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425"},{"name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"volume":16,"isi":1,"article_processing_charge":"No","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2102.11552"}]},{"main_file_link":[{"url":"https://doi.org/10.1017/S1474748022000482","open_access":"1"}],"scopus_import":"1","publication_identifier":{"eissn":["1475-3030 "],"issn":["1474-7480"]},"article_processing_charge":"Yes (via OA deal)","isi":1,"project":[{"name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_updated":"2023-08-02T06:55:10Z","year":"2022","date_created":"2021-09-15T10:06:48Z","quality_controlled":"1","author":[{"full_name":"Derenthal, Ulrich","first_name":"Ulrich","last_name":"Derenthal"},{"orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","first_name":"Florian Alexander"}],"publication":"Journal of the Institute of Mathematics of Jussieu","date_published":"2022-11-10T00:00:00Z","oa_version":"Published Version","external_id":{"isi":["000881319200001"],"arxiv":["2109.06778"]},"type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"publisher":"Cambridge University Press","doi":"10.1017/S1474748022000482","citation":{"ista":"Derenthal U, Wilsch FA. 2022. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu.","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>.","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>","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>"},"keyword":["Integral points","del Pezzo surface","universal torsor","Manin’s conjecture"],"day":"10","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"}],"status":"public","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.","department":[{"_id":"TiBr"}],"article_type":"original","publication_status":"epub_ahead","oa":1,"title":"Integral points on singular del Pezzo surfaces","month":"11","_id":"10018","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"day":"22","article_processing_charge":"No","keyword":["Integral point","toric variety","Manin's conjecture"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2202.10909"}],"citation":{"short":"F.A. Wilsch, ArXiv (n.d.).","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>","ista":"Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.","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>","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>.","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>."},"year":"2022","date_created":"2022-02-23T09:04:43Z","date_updated":"2023-05-03T07:46:35Z","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","grant_number":"P32428","call_identifier":"FWF"}],"article_number":"2202.10909","status":"public","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."}],"oa_version":"Preprint","external_id":{"arxiv":["2202.10909"]},"date_published":"2022-02-22T00:00:00Z","department":[{"_id":"TiBr"}],"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.","publication":"arXiv","author":[{"orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","first_name":"Florian Alexander"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.48550/arXiv.2202.10909","_id":"10788","month":"02","oa":1,"title":"Integral points of bounded height on a certain toric variety","publication_status":"submitted","arxiv":1,"language":[{"iso":"eng"}],"type":"preprint"}]