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Title: Fano 3-folds in codimension 4, Tom and Jerry. Part I
Authors: Brown, Gavin
Kerber, Michael
Reid, Miles
Keywords: Mori theory
Fano 3-fold
Sarkisov program
Issue Date: 2012
Publisher: Cambridge University Press / © Foundation Compositio Mathematica
Citation: BROWN, G., KERBER, M. and REID, M., 2012. Fano 3-folds in codimension 4, Tom and Jerry. Part I. Compositio Mathematica, 148 (4), pp. 1171 - 1194.
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.
Description: This article is closed access.
Sponsor: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
Version: Published
DOI: 10.1112/S0010437X11007226
URI: https://dspace.lboro.ac.uk/2134/15875
Publisher Link: http://dx.doi.org/10.1112/S0010437X11007226
ISSN: 0010-437X
Appears in Collections:Closed Access (Maths)

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