{"title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","_id":"3120","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T12:01:30Z","month":"07","date_updated":"2021-01-12T07:41:12Z","page":"1171 - 1194","volume":148,"type":"journal_article","year":"2012","author":[{"first_name":"Gavin","full_name":"Brown, Gavin","last_name":"Brown"},{"orcid":"0000-0002-8030-9299","last_name":"Kerber","full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael"},{"full_name":"Reid, Miles","last_name":"Reid","first_name":"Miles"}],"acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","oa_version":"Preprint","oa":1,"publication_status":"published","intvolume":"       148","quality_controlled":"1","publication":"Compositio Mathematica","day":"01","status":"public","date_published":"2012-07-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1009.4313"}],"doi":"10.1112/S0010437X11007226","scopus_import":1,"citation":{"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.","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>.","short":"G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 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>.","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.","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>"},"abstract":[{"lang":"eng","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."}],"publisher":"Cambridge University Press","publist_id":"3579","language":[{"iso":"eng"}],"issue":"4","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"}