[{"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.","ddc":["510"],"date_updated":"2023-08-01T14:51:57Z","citation":{"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>.","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.","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>","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>.","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."},"year":"2023","isi":1,"external_id":{"arxiv":["1810.06882"],"isi":["000996014700004"]},"doi":"10.2140/ant.2023.17.719","arxiv":1,"day":"12","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"}],"page":"719-748","quality_controlled":"1","file_date_updated":"2023-05-30T08:05:22Z","publisher":"Mathematical Sciences Publishers","article_type":"original","_id":"13091","scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"}],"issue":"3","publication_status":"published","date_created":"2023-05-28T22:01:02Z","department":[{"_id":"TiBr"}],"article_processing_charge":"No","title":"Free rational curves on low degree hypersurfaces and the circle method","intvolume":"        17","file":[{"checksum":"5d5d67b235905650e33cf7065d7583b4","file_size":1430719,"date_created":"2023-05-30T08:05:22Z","file_name":"2023_AlgebraNumberTheory_Browning.pdf","content_type":"application/pdf","date_updated":"2023-05-30T08:05:22Z","success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"13101"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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)"},"date_published":"2023-04-12T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"oa":1,"language":[{"iso":"eng"}],"publication":"Algebra and Number Theory","has_accepted_license":"1","oa_version":"Published Version","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"}],"month":"04"},{"department":[{"_id":"TiBr"}],"article_processing_charge":"No","date_created":"2021-02-25T09:56:57Z","publication_status":"published","intvolume":"        16","title":"Equidistribution and freeness on Grassmannians","scopus_import":"1","_id":"9199","issue":"10","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal","last_name":"Horesh","full_name":"Horesh, Tal"},{"last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"publisher":"Mathematical Sciences Publishers","article_type":"original","quality_controlled":"1","page":"2385-2407","day":"01","doi":"10.2140/ant.2022.16.2385","arxiv":1,"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."}],"citation":{"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>.","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>","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>","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>."},"year":"2022","date_updated":"2023-08-02T06:46:38Z","external_id":{"arxiv":["2102.11552"],"isi":["000961514100004"]},"isi":1,"volume":16,"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":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","name":"Between rational and integral points","grant_number":"EP-P026710-2"},{"name":"New frontiers of the Manin conjecture","grant_number":"P32428","call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","month":"12","publication":"Algebra & Number Theory","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"oa":1,"type":"journal_article","date_published":"2022-12-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2102.11552"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public"}]