[{"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."}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2202.10909"}],"publication_status":"submitted","day":"22","article_processing_charge":"No","author":[{"last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425","first_name":"Florian Alexander","orcid":"0000-0001-7302-8256"}],"doi":"10.48550/arXiv.2202.10909","title":"Integral points of bounded height on a certain toric variety","oa_version":"Preprint","_id":"10788","date_updated":"2023-05-03T07:46:35Z","date_created":"2022-02-23T09:04:43Z","type":"preprint","oa":1,"publication":"arXiv","status":"public","language":[{"iso":"eng"}],"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","grant_number":"P32428","call_identifier":"FWF"}],"citation":{"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>.","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>.","ista":"Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv, 2202.10909.","short":"F.A. Wilsch, ArXiv (n.d.).","ieee":"F. A. Wilsch, “Integral points of bounded height on a certain toric variety,” <i>arXiv</i>. .","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>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","date_published":"2022-02-22T00:00:00Z","year":"2022","month":"02","arxiv":1,"external_id":{"arxiv":["2202.10909"]},"department":[{"_id":"TiBr"}],"article_number":"2202.10909","keyword":["Integral point","toric variety","Manin's conjecture"]},{"issue":"10","citation":{"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.","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>","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>.","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>","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.","short":"T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &#38; Number Theory 16 (2022) 2385–2407."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"TiBr"}],"month":"12","arxiv":1,"publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"publication_status":"published","intvolume":"        16","abstract":[{"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.","lang":"eng"}],"volume":16,"article_type":"original","date_created":"2021-02-25T09:56:57Z","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","full_name":"Horesh, Tal","last_name":"Horesh","first_name":"Tal"},{"first_name":"Florian Alexander","orcid":"0000-0001-7302-8256","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"scopus_import":"1","day":"01","oa_version":"Preprint","title":"Equidistribution and freeness on Grassmannians","date_published":"2022-12-01T00:00:00Z","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.","project":[{"grant_number":"EP-P026710-2","name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"Algebra & Number Theory","isi":1,"year":"2022","external_id":{"isi":["000961514100004"],"arxiv":["2102.11552"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2102.11552"}],"quality_controlled":"1","page":"2385-2407","date_updated":"2023-08-02T06:46:38Z","_id":"9199","type":"journal_article","doi":"10.2140/ant.2022.16.2385","article_processing_charge":"No","publisher":"Mathematical Sciences Publishers"},{"publication_status":"epub_ahead","publication_identifier":{"issn":["1474-7480"],"eissn":["1475-3030 "]},"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"}],"article_type":"original","date_created":"2021-09-15T10:06:48Z","title":"Integral points on singular del Pezzo surfaces","oa_version":"Published Version","author":[{"last_name":"Derenthal","full_name":"Derenthal, Ulrich","first_name":"Ulrich"},{"orcid":"0000-0001-7302-8256","first_name":"Florian Alexander","last_name":"Wilsch","id":"560601DA-8D36-11E9-A136-7AC1E5697425","full_name":"Wilsch, Florian Alexander"}],"scopus_import":"1","day":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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>","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>.","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>","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.","short":"U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu (2022)."},"language":[{"iso":"eng"}],"oa":1,"department":[{"_id":"TiBr"}],"arxiv":1,"month":"11","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S1474748022000482"}],"type":"journal_article","date_updated":"2023-08-02T06:55:10Z","_id":"10018","publisher":"Cambridge University Press","doi":"10.1017/S1474748022000482","article_processing_charge":"Yes (via OA deal)","date_published":"2022-11-10T00:00:00Z","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.","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"New frontiers of the Manin conjecture","grant_number":"P32428"}],"publication":"Journal of the Institute of Mathematics of Jussieu","status":"public","keyword":["Integral points","del Pezzo surface","universal torsor","Manin’s conjecture"],"external_id":{"arxiv":["2109.06778"],"isi":["000881319200001"]},"isi":1,"year":"2022"},{"volume":28,"article_type":"original","date_created":"2023-03-28T09:21:09Z","author":[{"first_name":"Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D"}],"day":"24","title":"Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5","oa_version":"Published Version","publication_identifier":{"issn":["1076-9803"]},"publication_status":"published","file_date_updated":"2023-03-30T07:09:35Z","has_accepted_license":"1","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)"},"abstract":[{"text":"An improved asymptotic formula is established for the number of rational points of bounded height on the split smooth del Pezzo surface of degree 5. The proof uses the five conic bundle structures on the surface.","lang":"eng"}],"intvolume":"        28","department":[{"_id":"TiBr"}],"file":[{"file_id":"12778","file_size":897267,"date_created":"2023-03-30T07:09:35Z","date_updated":"2023-03-30T07:09:35Z","creator":"dernst","relation":"main_file","checksum":"c01e8291794a1bdb7416aa103cb68ef8","success":1,"file_name":"2022_NYJM_Browning.pdf","access_level":"open_access","content_type":"application/pdf"}],"month":"08","citation":{"short":"T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.","ieee":"T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5,” <i>New York Journal of Mathematics</i>, vol. 28. State University of New York, pp. 1193–1229, 2022.","ama":"Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. <i>New York Journal of Mathematics</i>. 2022;28:1193-1229.","mla":"Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>, vol. 28, State University of New York, 2022, pp. 1193–229.","apa":"Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. <i>New York Journal of Mathematics</i>. State University of New York.","ista":"Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.","chicago":"Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>. State University of New York, 2022."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"date_updated":"2023-10-18T07:59:13Z","_id":"12776","type":"journal_article","article_processing_charge":"No","publisher":"State University of New York","quality_controlled":"1","page":"1193 - 1229","ddc":["510"],"year":"2022","acknowledgement":"This work was begun while the author was participating in the programme on \"Diophantine equations\" at the Hausdorff Research Institute for Mathematics in Bonn in 2009. The hospitality and financial support of the institute is gratefully acknowledged. The idea of using conic bundles to study the split del Pezzo surface of degree 5 was explained to the author by Professor Salberger. The author is very grateful to him for his input into this project and also to Shuntaro Yamagishi for many useful comments on an earlier version of this manuscript. While working on this paper the author was supported by FWF grant P32428-N35.","date_published":"2022-08-24T00:00:00Z","project":[{"call_identifier":"FWF","grant_number":"P32428","name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"publication":"New York Journal of Mathematics","status":"public"},{"department":[{"_id":"TiBr"}],"month":"01","arxiv":1,"issue":"1","citation":{"apa":"Browning, T. D., &#38; Heath-Brown, R. (2021). The geometric sieve for quadrics. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>","mla":"Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>.","chicago":"Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>. De Gruyter, 2021. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>.","ista":"Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum Mathematicum. 33(1), 147–165.","ieee":"T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” <i>Forum Mathematicum</i>, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.","short":"T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.","ama":"Browning TD, Heath-Brown R. The geometric sieve for quadrics. <i>Forum Mathematicum</i>. 2021;33(1):147-165. doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"volume":33,"article_type":"original","date_created":"2020-11-08T23:01:25Z","author":[{"last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"first_name":"Roger","full_name":"Heath-Brown, Roger","last_name":"Heath-Brown"}],"scopus_import":"1","day":"01","oa_version":"Preprint","title":"The geometric sieve for quadrics","publication_status":"published","publication_identifier":{"eissn":["1435-5337"],"issn":["0933-7741"]},"intvolume":"        33","abstract":[{"lang":"eng","text":"We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros."}],"isi":1,"year":"2021","external_id":{"isi":["000604750900008"],"arxiv":["2003.09593"]},"date_published":"2021-01-01T00:00:00Z","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture","call_identifier":"FWF"}],"status":"public","publication":"Forum Mathematicum","date_updated":"2023-10-17T07:39:01Z","_id":"8742","type":"journal_article","doi":"10.1515/forum-2020-0074","article_processing_charge":"No","publisher":"De Gruyter","main_file_link":[{"url":"https://arxiv.org/abs/2003.09593","open_access":"1"}],"quality_controlled":"1","page":"147-165"}]