---
_id: '3120'
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.
acknowledgement: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
article_processing_charge: No
arxiv: 1
author:
- first_name: Gavin
  full_name: Brown, Gavin
  last_name: Brown
- first_name: Michael
  full_name: Kerber, Michael
  id: 36E4574A-F248-11E8-B48F-1D18A9856A87
  last_name: Kerber
  orcid: 0000-0002-8030-9299
- first_name: Miles
  full_name: Reid, Miles
  last_name: Reid
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>
  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.
  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.
date_created: 2018-12-11T12:01:30Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2025-09-30T07:59:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/S0010437X11007226
external_id:
  arxiv:
  - '1009.4313'
  isi:
  - '000307176400007'
intvolume: '       148'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1009.4313
month: '07'
oa: 1
oa_version: Preprint
page: 1171 - 1194
publication: Compositio Mathematica
publication_status: published
publisher: Cambridge University Press
publist_id: '3579'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fano 3 folds in codimension 4 Tom and Jerry Part I
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 148
year: '2012'
...