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Fano 3-folds in codimension 4, Tom and Jerry. Part I
journal contribution
posted on 2014-09-17, 13:22 authored by Gavin Brown, Michael Kerber, Miles ReidWe 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.
Funding
This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
History
School
- Science
Department
- Mathematical Sciences
Published in
COMPOSITIO MATHEMATICAVolume
148Issue
4Pages
1171 - 1194 (24)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.Publisher
Cambridge University Press / © Foundation Compositio MathematicaVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2012Notes
This article is closed access.ISSN
0010-437XPublisher version
Language
- en