Fano 3 folds in codimension 4 Tom and Jerry Part I Brown, Gavin Kerber, Michael ; https://orcid.org/0000-0002-8030-9299 Reid, Miles 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. Cambridge University Press 2012 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/3120 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/S0010437X11007226 info:eu-repo/semantics/altIdentifier/wos/000307176400007 info:eu-repo/semantics/altIdentifier/arxiv/1009.4313 info:eu-repo/semantics/openAccess