{"publisher":" Mathematical Sciences Publishers","oa_version":"Preprint","oa":1,"date_created":"2018-12-11T11:45:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Rational curves on smooth hypersurfaces of low degree","quality_controlled":"1","status":"public","article_processing_charge":"No","month":"09","date_updated":"2024-03-05T11:43:38Z","type":"journal_article","day":"07","abstract":[{"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.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1611.00553","open_access":"1"}],"date_published":"2017-09-07T00:00:00Z","publication_status":"published","extern":"1","issue":"7","year":"2017","intvolume":"        11","volume":11,"publist_id":"7637","acknowledgement":"While working on this paper the first author was supported by ERC grant 306457.","external_id":{"arxiv":["1611.00553"]},"publication_identifier":{"eissn":["1944-7833"]},"author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Vishe, Pankaj","first_name":"Pankaj","last_name":"Vishe"}],"publication":"Geometric Methods in Algebra and Number Theory","page":"1657 - 1675","doi":"10.2140/ant.2017.11.1657","_id":"265","language":[{"iso":"eng"}],"citation":{"short":"T.D. Browning, P. Vishe, Geometric Methods in Algebra and Number Theory 11 (2017) 1657–1675.","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>","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>","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.","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>.","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.","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>."},"article_type":"original"}