Fano 3-folds in P2xP2 format, Tom and Jerry

Brown, Gavin and Kasprzyk, Alexander M. and Qureshi, Imran (2018) Fano 3-folds in P2xP2 format, Tom and Jerry. European Journal of Mathematics, 4 (1). pp. 51-72. ISSN 2199-675X

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Available under Licence Creative Commons Attribution.
Download (497kB) | Preview


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.

Item Type: Article
Keywords: Fano 3-fold; Segre embedding; Gorenstein format
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1007/s40879-017-0200-2
Depositing User: Kasprzyk, Dr Alexander
Date Deposited: 01 Sep 2017 14:52
Last Modified: 09 Mar 2018 10:02

Actions (Archive Staff Only)

Edit View Edit View