{"publisher":" Mathematical Sciences Publishers","citation":{"chicago":"Browning, Timothy D, and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” Geometric Methods in Algebra and Number Theory. Mathematical Sciences Publishers, 2017. https://doi.org/10.2140/ant.2017.11.1657.","mla":"Browning, Timothy D., and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7, Mathematical Sciences Publishers, 2017, pp. 1657–75, doi:10.2140/ant.2017.11.1657.","ieee":"T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low degree,” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7. Mathematical Sciences Publishers, pp. 1657–1675, 2017.","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.","ama":"Browning TD, Vishe P. Rational curves on smooth hypersurfaces of low degree. Geometric Methods in Algebra and Number Theory. 2017;11(7):1657-1675. doi:10.2140/ant.2017.11.1657","apa":"Browning, T. D., & Vishe, P. (2017). Rational curves on smooth hypersurfaces of low degree. Geometric Methods in Algebra and Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2017.11.1657"},"status":"public","volume":11,"year":"2017","article_type":"original","day":"07","intvolume":" 11","oa_version":"Preprint","title":"Rational curves on smooth hypersurfaces of low degree","author":[{"last_name":"Browning","full_name":"Browning, Timothy D","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"}],"publication_identifier":{"eissn":["1944-7833"]},"page":"1657 - 1675","_id":"265","publist_id":"7637","article_processing_charge":"No","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1611.00553","open_access":"1"}],"doi":"10.2140/ant.2017.11.1657","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:45:30Z","type":"journal_article","publication":"Geometric Methods in Algebra and Number Theory","corr_author":"1","quality_controlled":"1","issue":"7","month":"09","extern":"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."}],"publication_status":"published","external_id":{"arxiv":["1611.00553"]},"date_updated":"2024-10-09T20:58:17Z","date_published":"2017-09-07T00:00:00Z","acknowledgement":"While working on this paper the first author was supported by ERC grant 306457."}