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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
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, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Compositio Mathematica | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0010-437X | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| 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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