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Fano 3-folds in P2xP2 format, Tom and Jerry

Brown, Gavin; Kasprzyk, Alexander M.; Qureshi, Imran

Authors

Gavin Brown

Alexander M. Kasprzyk A.M.Kasprzyk@nottingham.ac.uk

Imran Qureshi



Abstract

We study Q-factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of P^2xP^2. These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state of classification in three different ways. Some families arise as unprojections of degenerations of complete intersections, where the generic unprojection is a known prime Fano 3-fold in codimension 3; these are new, and an analysis of their Gorenstein projections reveals yet other new families. Others represent the "second Tom" unprojection families already known in codimension 4, and we show that every such family contains one of our models. Yet others have no easy Gorenstein projection analysis at all, so prove the existence of Fano components on their Hilbert scheme.

Journal Article Type Article
Publication Date Mar 30, 2018
Journal European Journal of Mathematics
Electronic ISSN 2199-675X
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 4
Issue 1
APA6 Citation Brown, G., Kasprzyk, A. M., & Qureshi, I. (2018). Fano 3-folds in P2xP2 format, Tom and Jerry. European Journal of Mathematics, 4(1), https://doi.org/10.1007/s40879-017-0200-2
DOI https://doi.org/10.1007/s40879-017-0200-2
Keywords Fano 3-fold; Segre embedding; Gorenstein format
Publisher URL https://link.springer.com/article/10.1007%2Fs40879-017-0200-2
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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