article published yes Gavin Brown author Michael Kerber author 36E4574A-F248-11E8-B48F-1D18A9856A870000-0002-8030-9299 Miles Reid author HeEd department 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 Press2012 eng 1009.4313 00030717640000710.1112/S0010437X11007226 14841171 - 1194 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>. 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> Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194. 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> 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. G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194. 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>. 31202018-12-11T12:01:30Z2025-09-30T07:59:55Z