{"acknowledgement":"While working on this paper the first two authors were supported by EPSRC grant EP/E053262/1, and the first author was further supported by ERC grant 306457.","citation":{"ama":"Browning TD, Matthiesen L, Skorobogatov A. Rational points on pencils of conics and quadrics with many degenerate fibres. <i>Annals of Mathematics</i>. 2014;180(1):381-402. doi:<a href=\"https://doi.org/10.4007/annals.2014.180.1.8\">https://doi.org/10.4007/annals.2014.180.1.8</a>","mla":"Browning, Timothy D., et al. “Rational Points on Pencils of Conics and Quadrics with Many Degenerate Fibres.” <i>Annals of Mathematics</i>, vol. 180, no. 1, John Hopkins University Press, 2014, pp. 381–402, doi:<a href=\"https://doi.org/10.4007/annals.2014.180.1.8\">https://doi.org/10.4007/annals.2014.180.1.8</a>.","short":"T.D. Browning, L. Matthiesen, A. Skorobogatov, Annals of Mathematics 180 (2014) 381–402.","ieee":"T. D. Browning, L. Matthiesen, and A. Skorobogatov, “Rational points on pencils of conics and quadrics with many degenerate fibres,” <i>Annals of Mathematics</i>, vol. 180, no. 1. John Hopkins University Press, pp. 381–402, 2014.","ista":"Browning TD, Matthiesen L, Skorobogatov A. 2014. Rational points on pencils of conics and quadrics with many degenerate fibres. Annals of Mathematics. 180(1), 381–402.","chicago":"Browning, Timothy D, Lilian Matthiesen, and Alexei Skorobogatov. “Rational Points on Pencils of Conics and Quadrics with Many Degenerate Fibres.” <i>Annals of Mathematics</i>. John Hopkins University Press, 2014. <a href=\"https://doi.org/10.4007/annals.2014.180.1.8\">https://doi.org/10.4007/annals.2014.180.1.8</a>.","apa":"Browning, T. D., Matthiesen, L., &#38; Skorobogatov, A. (2014). Rational points on pencils of conics and quadrics with many degenerate fibres. <i>Annals of Mathematics</i>. John Hopkins University Press. <a href=\"https://doi.org/10.4007/annals.2014.180.1.8\">https://doi.org/10.4007/annals.2014.180.1.8</a>"},"date_created":"2018-12-11T11:45:25Z","month":"07","page":"381 - 402","status":"public","year":"2014","publisher":"John Hopkins University Press","day":"01","date_published":"2014-07-01T00:00:00Z","oa":1,"volume":180,"date_updated":"2021-01-12T06:57:44Z","publist_id":"7655","type":"journal_article","extern":1,"intvolume":"       180","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Timothy Browning"},{"last_name":"Matthiesen","full_name":"Matthiesen, Lilian","first_name":"Lilian"},{"full_name":"Skorobogatov, Alexei N","first_name":"Alexei","last_name":"Skorobogatov"}],"doi":"https://doi.org/10.4007/annals.2014.180.1.8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1209.0207"}],"_id":"248","title":"Rational points on pencils of conics and quadrics with many degenerate fibres","quality_controlled":0,"publication_status":"published","issue":"1","publication":"Annals of Mathematics","abstract":[{"lang":"eng","text":"For any pencil of conics or higher-dimensional quadrics over ℚ, with all degenerate fibres defined over ℚ, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over ℚ, which is a consequence of recent advances in additive combinatorics."}]}