Fano 3 folds in codimension 4 Tom and Jerry Part I Journal Article

Author(s): Brown, Gavin; Kerber, Michael; Reid, Miles
Article Title: Fano 3 folds in codimension 4 Tom and Jerry Part I
Affiliation IST Austria
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.
Keywords: Fano 3-fold; Mori theory; Sarkisov program; unprojection
Journal Title: Compositio Mathematica
Volume: 148
Issue 4
ISSN: 0010-437X
Publisher: Cambridge University Press  
Date Published: 2012-07-01
Start Page: 1171
End Page: 1194
Sponsor: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.
DOI: 10.1112/S0010437X11007226
Open access: yes (repository)