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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 Reid
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.

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 MATHEMATICA

Volume

148

Issue

4

Pages

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 Mathematica

Version

  • 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

2012

Notes

This article is closed access.

ISSN

0010-437X

Language

  • en

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