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

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 con...

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Main Authors: Gavin Brown, Michael Kerber, Miles Reid
Format: Default Article
Published: 2012
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Online Access:https://hdl.handle.net/2134/15875
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spelling rr-article-93767542012-01-01T00:00:00Z Fano 3-folds in codimension 4, Tom and Jerry. Part I Gavin Brown (1258149) Michael Kerber (7159538) Miles Reid (7159541) Other mathematical sciences not elsewhere classified Mori theory Fano 3-fold Unprojection Sarkisov program Mathematical Sciences not elsewhere classified 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. 2012-01-01T00:00:00Z Text Journal contribution 2134/15875 https://figshare.com/articles/journal_contribution/Fano_3-folds_in_codimension_4_Tom_and_Jerry_Part_I/9376754 CC BY-NC-ND 4.0
institution Loughborough University
collection Figshare
topic Other mathematical sciences not elsewhere classified
Mori theory
Fano 3-fold
Unprojection
Sarkisov program
Mathematical Sciences not elsewhere classified
spellingShingle Other mathematical sciences not elsewhere classified
Mori theory
Fano 3-fold
Unprojection
Sarkisov program
Mathematical Sciences not elsewhere classified
Gavin Brown
Michael Kerber
Miles Reid
Fano 3-folds in codimension 4, Tom and Jerry. Part I
description 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.
format Default
Article
author Gavin Brown
Michael Kerber
Miles Reid
author_facet Gavin Brown
Michael Kerber
Miles Reid
author_sort Gavin Brown (1258149)
title Fano 3-folds in codimension 4, Tom and Jerry. Part I
title_short Fano 3-folds in codimension 4, Tom and Jerry. Part I
title_full Fano 3-folds in codimension 4, Tom and Jerry. Part I
title_fullStr Fano 3-folds in codimension 4, Tom and Jerry. Part I
title_full_unstemmed Fano 3-folds in codimension 4, Tom and Jerry. Part I
title_sort fano 3-folds in codimension 4, tom and jerry. part i
publishDate 2012
url https://hdl.handle.net/2134/15875
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