[{"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"13101","file_size":1430719,"checksum":"5d5d67b235905650e33cf7065d7583b4","date_created":"2023-05-30T08:05:22Z","file_name":"2023_AlgebraNumberTheory_Browning.pdf","content_type":"application/pdf","date_updated":"2023-05-30T08:05:22Z"}],"oa":1,"publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"date_published":"2023-04-12T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"month":"04","oa_version":"Published Version","project":[{"name":"Between rational and integral points","grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425"}],"publication":"Algebra and Number Theory","has_accepted_license":"1","ddc":["510"],"volume":17,"acknowledgement":"The authors are grateful to Paul Nelson, Per Salberger and Jason Starr for useful comments. While working on this paper the first author was supported by EPRSC grant EP/P026710/1. The research was partially conducted during the period the second author served as a Clay Research Fellow, and partially conducted during the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.","abstract":[{"text":"We use a function field version of the Hardy–Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the dimension of the singular locus of the moduli space of rational curves on such hypersurfaces and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin conjecture in terms of slopes with respect to the tangent bundle.","lang":"eng"}],"arxiv":1,"doi":"10.2140/ant.2023.17.719","day":"12","isi":1,"external_id":{"arxiv":["1810.06882"],"isi":["000996014700004"]},"date_updated":"2023-08-01T14:51:57Z","citation":{"ista":"Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 17(3), 719–748.","short":"T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748.","mla":"Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” <i>Algebra and Number Theory</i>, vol. 17, no. 3, Mathematical Sciences Publishers, 2023, pp. 719–48, doi:<a href=\"https://doi.org/10.2140/ant.2023.17.719\">10.2140/ant.2023.17.719</a>.","ieee":"T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces and the circle method,” <i>Algebra and Number Theory</i>, vol. 17, no. 3. Mathematical Sciences Publishers, pp. 719–748, 2023.","chicago":"Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” <i>Algebra and Number Theory</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/ant.2023.17.719\">https://doi.org/10.2140/ant.2023.17.719</a>.","apa":"Browning, T. D., &#38; Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. <i>Algebra and Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2023.17.719\">https://doi.org/10.2140/ant.2023.17.719</a>","ama":"Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. <i>Algebra and Number Theory</i>. 2023;17(3):719-748. doi:<a href=\"https://doi.org/10.2140/ant.2023.17.719\">10.2140/ant.2023.17.719</a>"},"year":"2023","article_type":"original","publisher":"Mathematical Sciences Publishers","file_date_updated":"2023-05-30T08:05:22Z","page":"719-748","quality_controlled":"1","title":"Free rational curves on low degree hypersurfaces and the circle method","intvolume":"        17","publication_status":"published","department":[{"_id":"TiBr"}],"date_created":"2023-05-28T22:01:02Z","article_processing_charge":"No","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Sawin, Will","last_name":"Sawin","first_name":"Will"}],"issue":"3","_id":"13091","scopus_import":"1"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2102.11552"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2022-12-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"oa":1,"language":[{"iso":"eng"}],"publication":"Algebra & Number Theory","oa_version":"Preprint","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"},{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"month":"12","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.","volume":16,"date_updated":"2023-08-02T06:46:38Z","year":"2022","citation":{"ista":"Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra &#38; Number Theory. 16(10), 2385–2407.","short":"T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &#38; Number Theory 16 (2022) 2385–2407.","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>.","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.","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>.","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>","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>"},"isi":1,"external_id":{"arxiv":["2102.11552"],"isi":["000961514100004"]},"arxiv":1,"doi":"10.2140/ant.2022.16.2385","day":"01","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"}],"page":"2385-2407","quality_controlled":"1","publisher":"Mathematical Sciences Publishers","article_type":"original","_id":"9199","scopus_import":"1","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Horesh, Tal","first_name":"Tal","last_name":"Horesh","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"issue":"10","publication_status":"published","article_processing_charge":"No","department":[{"_id":"TiBr"}],"date_created":"2021-02-25T09:56:57Z","title":"Equidistribution and freeness on Grassmannians","intvolume":"        16"},{"volume":11,"acknowledgement":"While working on this paper the first author was supported by ERC grant 306457.","extern":"1","citation":{"mla":"Browning, Timothy D., and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” <i>Geometric Methods in Algebra and Number Theory</i>, vol. 11, no. 7,  Mathematical Sciences Publishers, 2017, pp. 1657–75, doi:<a href=\"https://doi.org/10.2140/ant.2017.11.1657\">10.2140/ant.2017.11.1657</a>.","short":"T.D. Browning, P. Vishe, Geometric Methods in Algebra and Number Theory 11 (2017) 1657–1675.","ista":"Browning TD, Vishe P. 2017. Rational curves on smooth hypersurfaces of low degree. Geometric Methods in Algebra and Number Theory. 11(7), 1657–1675.","apa":"Browning, T. D., &#38; Vishe, P. (2017). Rational curves on smooth hypersurfaces of low degree. <i>Geometric Methods in Algebra and Number Theory</i>.  Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2017.11.1657\">https://doi.org/10.2140/ant.2017.11.1657</a>","ama":"Browning TD, Vishe P. Rational curves on smooth hypersurfaces of low degree. <i>Geometric Methods in Algebra and Number Theory</i>. 2017;11(7):1657-1675. doi:<a href=\"https://doi.org/10.2140/ant.2017.11.1657\">10.2140/ant.2017.11.1657</a>","ieee":"T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low degree,” <i>Geometric Methods in Algebra and Number Theory</i>, vol. 11, no. 7.  Mathematical Sciences Publishers, pp. 1657–1675, 2017.","chicago":"Browning, Timothy D, and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” <i>Geometric Methods in Algebra and Number Theory</i>.  Mathematical Sciences Publishers, 2017. <a href=\"https://doi.org/10.2140/ant.2017.11.1657\">https://doi.org/10.2140/ant.2017.11.1657</a>."},"year":"2017","date_updated":"2024-03-05T11:43:38Z","external_id":{"arxiv":["1611.00553"]},"day":"07","doi":"10.2140/ant.2017.11.1657","arxiv":1,"abstract":[{"lang":"eng","text":"We establish the dimension and irreducibility of the moduli space of rational curves (of fixed degree) on arbitrary smooth hypersurfaces of sufficiently low degree. A spreading out argument reduces the problem to hypersurfaces defined over finite fields of large cardinality, which can then be tackled using a function field version of the Hardy-Littlewood circle method, in which particular care is taken to ensure uniformity in the size of the underlying finite field."}],"quality_controlled":"1","page":"1657 - 1675","publisher":" Mathematical Sciences Publishers","article_type":"original","_id":"265","issue":"7","author":[{"first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Vishe","first_name":"Pankaj","full_name":"Vishe, Pankaj"}],"article_processing_charge":"No","date_created":"2018-12-11T11:45:30Z","publication_status":"published","intvolume":"        11","title":"Rational curves on smooth hypersurfaces of low degree","main_file_link":[{"url":"https://arxiv.org/abs/1611.00553","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_published":"2017-09-07T00:00:00Z","publication_identifier":{"eissn":["1944-7833"]},"oa":1,"publist_id":"7637","language":[{"iso":"eng"}],"publication":"Geometric Methods in Algebra and Number Theory","oa_version":"Preprint","month":"09"}]