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Fano 3-folds in codimension 4, Tom and Jerry. Part I

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Brown, Gavin, Kerber, Michael and Reid, Miles (2012) Fano 3-folds in codimension 4, Tom and Jerry. Part I. Compositio Mathematica, Volume 148 (Number 4). pp. 1171-1194. doi:10.1112/S0010437X11007226

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Official URL: http://dx.doi.org/10.1112/S0010437X11007226

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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 Altınok’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.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Compositio Mathematica
Publisher: Cambridge University Press
ISSN: 0010-437X
Official Date: 2012
Dates:
DateEvent
2012Published
Volume: Volume 148
Number: Number 4
Page Range: pp. 1171-1194
DOI: 10.1112/S0010437X11007226
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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