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

  • Gavin Brown (a1), Michael Kerber (a2) and Miles Reid (a3)
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.

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References
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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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