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

Published online by Cambridge University Press:  14 May 2012


Gavin Brown
Affiliation:
School of Mathematics, Loughborough University, LE11 3TU, UK (email: g.d.brown@lboro.ac.uk)
Michael Kerber
Affiliation:
Institute of Science and Technology (IST) Austria, 3400 Klosterneuburg, Austria (email: michael.kerber@ist.ac.at)
Miles Reid
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (email: miles.reid@warwick.ac.uk)

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.


MSC classification


Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2012

References

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