--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Gavin foaf_name: Brown, Gavin foaf_surname: Brown - foaf_Person: foaf_givenName: Michael foaf_name: Kerber, Michael foaf_surname: Kerber foaf_workInfoHomepage: http://www.librecat.org/personId=36E4574A-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8030-9299 - foaf_Person: foaf_givenName: Miles foaf_name: Reid, Miles foaf_surname: Reid bibo_doi: 10.1112/S0010437X11007226 bibo_issue: '4' bibo_volume: 148 dct_date: 2012^xs_gYear dct_language: eng dct_publisher: Cambridge University Press@ dct_title: Fano 3 folds in codimension 4 Tom and Jerry Part I@ ...