[{"citation":{"mla":"Browning, Timothy D. “Many Cubic Surfaces Contain Rational Points.” <i>Mathematika</i>, vol. 63, no. 3, Cambridge University Press, 2017, pp. 818–39, doi:<a href=\"https://doi.org/10.1112/S0025579317000195\">10.1112/S0025579317000195</a>.","short":"T.D. Browning, Mathematika 63 (2017) 818–839.","ista":"Browning TD. 2017. Many cubic surfaces contain rational points. Mathematika. 63(3), 818–839.","ama":"Browning TD. Many cubic surfaces contain rational points. <i>Mathematika</i>. 2017;63(3):818-839. doi:<a href=\"https://doi.org/10.1112/S0025579317000195\">10.1112/S0025579317000195</a>","apa":"Browning, T. D. (2017). Many cubic surfaces contain rational points. <i>Mathematika</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/S0025579317000195\">https://doi.org/10.1112/S0025579317000195</a>","chicago":"Browning, Timothy D. “Many Cubic Surfaces Contain Rational Points.” <i>Mathematika</i>. Cambridge University Press, 2017. <a href=\"https://doi.org/10.1112/S0025579317000195\">https://doi.org/10.1112/S0025579317000195</a>.","ieee":"T. D. Browning, “Many cubic surfaces contain rational points,” <i>Mathematika</i>, vol. 63, no. 3. Cambridge University Press, pp. 818–839, 2017."},"year":"2017","date_updated":"2024-03-05T11:49:27Z","external_id":{"arxiv":["1701.00525"]},"day":"29","arxiv":1,"doi":"10.1112/S0025579317000195","abstract":[{"text":"Building on recent work of Bhargava, Elkies and Schnidman and of Kriz and Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.","lang":"eng"}],"volume":63,"acknowledgement":"While working on this paper the author was supported by ERC grant 306457.","extern":"1","_id":"267","issue":"3","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","date_created":"2018-12-11T11:45:31Z","publication_status":"published","intvolume":"        63","title":"Many cubic surfaces contain rational points","quality_controlled":"1","page":"818 - 839","publisher":"Cambridge University Press","article_type":"original","type":"journal_article","date_published":"2017-11-29T00:00:00Z","publication_identifier":{"issn":["0025-5793"]},"publist_id":"7635","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.00525"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Mathematika","oa_version":"Preprint","month":"11","language":[{"iso":"eng"}]},{"issue":"1-2","author":[{"id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas","last_name":"Hausel","full_name":"Hausel, Tamas"},{"full_name":"Makai, Endre","first_name":"Endre","last_name":"Makai"},{"full_name":"Szücs, András","last_name":"Szücs","first_name":"András"}],"scopus_import":"1","_id":"1455","intvolume":"        47","title":"Inscribing cubes and covering by rhombic dodecahedra via equivariant topology","date_created":"2018-12-11T11:52:07Z","article_processing_charge":"No","publication_status":"published","quality_controlled":"1","page":"371 - 397","article_type":"original","publisher":"University College London","external_id":{"arxiv":["math/9906066"]},"citation":{"ista":"Hausel T, Makai E, Szücs A. 2000. Inscribing cubes and covering by rhombic dodecahedra via equivariant topology. Mathematika. 47(1–2), 371–397.","mla":"Hausel, Tamás, et al. “Inscribing Cubes and Covering by Rhombic Dodecahedra via Equivariant Topology.” <i>Mathematika</i>, vol. 47, no. 1–2, University College London, 2000, pp. 371–97, doi:<a href=\"https://doi.org/10.1112/S0025579300015965\">10.1112/S0025579300015965</a>.","short":"T. Hausel, E. Makai, A. Szücs, Mathematika 47 (2000) 371–397.","ieee":"T. Hausel, E. Makai, and A. Szücs, “Inscribing cubes and covering by rhombic dodecahedra via equivariant topology,” <i>Mathematika</i>, vol. 47, no. 1–2. University College London, pp. 371–397, 2000.","chicago":"Hausel, Tamás, Endre Makai, and András Szücs. “Inscribing Cubes and Covering by Rhombic Dodecahedra via Equivariant Topology.” <i>Mathematika</i>. University College London, 2000. <a href=\"https://doi.org/10.1112/S0025579300015965\">https://doi.org/10.1112/S0025579300015965</a>.","ama":"Hausel T, Makai E, Szücs A. Inscribing cubes and covering by rhombic dodecahedra via equivariant topology. <i>Mathematika</i>. 2000;47(1-2):371-397. doi:<a href=\"https://doi.org/10.1112/S0025579300015965\">10.1112/S0025579300015965</a>","apa":"Hausel, T., Makai, E., &#38; Szücs, A. (2000). Inscribing cubes and covering by rhombic dodecahedra via equivariant topology. <i>Mathematika</i>. University College London. <a href=\"https://doi.org/10.1112/S0025579300015965\">https://doi.org/10.1112/S0025579300015965</a>"},"year":"2000","date_updated":"2023-05-08T08:56:46Z","abstract":[{"text":"First, a special case of Knaster's problem is proved implying that each symmetric convex body in ℝ3 admits an inscribed cube. It is deduced from a theorem in equivariant topology, which says that there is no S4 - equivariant map from SO(3) to S2, where S4 acts on SO(3) on the right as the rotation group of the cube, and on S2 on the right as the symmetry group of the regular tetrahedron. Some generalizations are also given. Second, it is shown how the above non-existence theorem yields Makeev's conjecture in ℝ3 that each set in ℝ3 of diameter 1 can be covered by a rhombic dodecahedron, which has distance 1 between its opposite faces. This reveals an unexpected connection between inscribing cubes into symmetric bodies and covering sets by rhombic dodecahedra. Finally, a possible application of our second theorem to the Borsuk problem in ℝ3 is pointed out.","lang":"eng"}],"day":"01","arxiv":1,"doi":"10.1112/S0025579300015965","extern":"1","volume":47,"acknowledgement":"The research of the first author was partially supported by Trinity College, Cambridge, and that of all the authors by grants 23444, T-030012 and A 046/96, respectively, from the Hungarian National Foundation for Scientific Research.","publication":"Mathematika","month":"06","oa_version":"Preprint","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2000-06-01T00:00:00Z","publist_id":"5745","oa":1,"publication_identifier":{"issn":["0025-5793"]},"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"http://arxiv.org/abs/math/9906066","open_access":"1"}]}]