Fano 3 folds in codimension 4 Tom and Jerry Part I

G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.


Journal Article | Published | English
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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 Altinok'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 Copyright Foundation Compositio Mathematica.
Publishing Year
Date Published
2012-07-01
Journal Title
Compositio Mathematica
Acknowledgement
This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
Volume
148
Issue
4
Page
1171 - 1194
IST-REx-ID

Cite this

Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 2012;148(4):1171-1194. doi:10.1112/S0010437X11007226
Brown, G., Kerber, M., & Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica, 148(4), 1171–1194. https://doi.org/10.1112/S0010437X11007226
Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica 148, no. 4 (2012): 1171–94. https://doi.org/10.1112/S0010437X11007226.
G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” Compositio Mathematica, vol. 148, no. 4, pp. 1171–1194, 2012.
Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194.
Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:10.1112/S0010437X11007226.

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