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Fano 3-folds in P2×P2 format, Tom and Jerry

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Brown, Gavin, Kasprzyk, Alexander and Qureshi, Muhammad Imran (2018) Fano 3-folds in P2×P2 format, Tom and Jerry. European Journal of Mathematics, 4 (1). pp. 51-72. doi:10.1007/s40879-017-0200-2 ISSN 2199-675X.

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Official URL: https://doi.org/10.1007/s40879-017-0200-2

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Abstract

We study \({\mathbb {Q}}\) -factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of Open image in new window. 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: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Geometry, Algebraic, Gorenstein rings, Hilbert schemes
Journal or Publication Title: European Journal of Mathematics
Publisher: Springer
ISSN: 2199-675X
Official Date: March 2018
Dates:
DateEvent
March 2018Published
28 November 2017Available
30 August 2017Accepted
Volume: 4
Number: 1
Page Range: pp. 51-72
DOI: 10.1007/s40879-017-0200-2
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Description:

Please see publisher's version for correctly formatted formulae.

Date of first compliant deposit: 24 October 2017
Date of first compliant Open Access: 2 May 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/N022513/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
STG-MTH-1305Lahore University of Management Scienceshttp://dx.doi.org/10.13039/100010139
UNSPECIFIEDLondon Mathematical Societyhttp://dx.doi.org/10.13039/501100000608

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