Fano 3-folds in P2xP2 format, Tom and Jerry

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

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.

Citation

Brown, G., Kasprzyk, A. M., & Qureshi, I. (2018). Fano 3-folds in P2xP2 format, Tom and Jerry. European Journal of Mathematics, 4(1), 51-72. https://doi.org/10.1007/s40879-017-0200-2

• Journal Article Type: Article
• Acceptance Date: Aug 30, 2017
• Online Publication Date: Nov 28, 2017
• Publication Date: 2018-03
• Deposit Date: Sep 1, 2017
• Publicly Available Date: Nov 28, 2017
• Journal: European Journal of Mathematics
• Electronic ISSN: 2199-6768
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 1
• Pages: 51-72
• DOI: https://doi.org/10.1007/s40879-017-0200-2
• Keywords: Fano 3-fold; Segre embedding; Gorenstein format
• Public URL: https://nottingham-repository.worktribe.com/output/922090
• Publisher URL: https://link.springer.com/article/10.1007%2Fs40879-017-0200-2