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