{"date_updated":"2025-06-11T08:09:23Z","day":"01","date_published":"2012-07-01T00:00:00Z","oa_version":"Preprint","issue":"4","_id":"3120","department":[{"_id":"HeEd"}],"status":"public","doi":"10.1112/S0010437X11007226","year":"2012","volume":148,"publication_status":"published","title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","arxiv":1,"citation":{"ama":"Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. <i>Compositio Mathematica</i>. 2012;148(4):1171-1194. doi:<a href=\"https://doi.org/10.1112/S0010437X11007226\">10.1112/S0010437X11007226</a>","ista":"Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194.","apa":"Brown, G., Kerber, M., &#38; Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. <i>Compositio Mathematica</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/S0010437X11007226\">https://doi.org/10.1112/S0010437X11007226</a>","chicago":"Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” <i>Compositio Mathematica</i>. Cambridge University Press, 2012. <a href=\"https://doi.org/10.1112/S0010437X11007226\">https://doi.org/10.1112/S0010437X11007226</a>.","short":"G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.","ieee":"G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” <i>Compositio Mathematica</i>, vol. 148, no. 4. Cambridge University Press, pp. 1171–1194, 2012.","mla":"Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” <i>Compositio Mathematica</i>, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:<a href=\"https://doi.org/10.1112/S0010437X11007226\">10.1112/S0010437X11007226</a>."},"type":"journal_article","quality_controlled":"1","month":"07","publisher":"Cambridge University Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","abstract":[{"text":"We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica.","lang":"eng"}],"author":[{"full_name":"Brown, Gavin","first_name":"Gavin","last_name":"Brown"},{"last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299"},{"first_name":"Miles","last_name":"Reid","full_name":"Reid, Miles"}],"publist_id":"3579","date_created":"2018-12-11T12:01:30Z","external_id":{"arxiv":["1009.4313"]},"publication":"Compositio Mathematica","scopus_import":"1","language":[{"iso":"eng"}],"article_processing_charge":"No","page":"1171 - 1194","main_file_link":[{"url":"http://arxiv.org/abs/1009.4313","open_access":"1"}],"intvolume":"       148","oa":1}