Fano 3-folds in P2xP2 format, Tom and Jerry
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...
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| Format: | Article |
| Language: | English |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/45359/ |
| _version_ | 1848797116045983744 |
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| author | Brown, Gavin Kasprzyk, Alexander M. Qureshi, Imran |
| author_facet | Brown, Gavin Kasprzyk, Alexander M. Qureshi, Imran |
| author_sort | Brown, Gavin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:58:45Z |
| format | Article |
| id | nottingham-45359 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:58:45Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-453592018-03-09T10:02:44Z https://eprints.nottingham.ac.uk/45359/ Fano 3-folds in P2xP2 format, Tom and Jerry Brown, Gavin Kasprzyk, Alexander M. Qureshi, Imran 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. Springer 2018-03-30 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/45359/8/10.1007%252Fs40879-017-0200-2.pdf Brown, Gavin, 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 Fano 3-fold; Segre embedding; Gorenstein format https://link.springer.com/article/10.1007%2Fs40879-017-0200-2 doi:10.1007/s40879-017-0200-2 doi:10.1007/s40879-017-0200-2 |
| spellingShingle | Fano 3-fold; Segre embedding; Gorenstein format Brown, Gavin Kasprzyk, Alexander M. Qureshi, Imran Fano 3-folds in P2xP2 format, Tom and Jerry |
| title | Fano 3-folds in P2xP2 format, Tom and Jerry |
| title_full | Fano 3-folds in P2xP2 format, Tom and Jerry |
| title_fullStr | Fano 3-folds in P2xP2 format, Tom and Jerry |
| title_full_unstemmed | Fano 3-folds in P2xP2 format, Tom and Jerry |
| title_short | Fano 3-folds in P2xP2 format, Tom and Jerry |
| title_sort | fano 3-folds in p2xp2 format, tom and jerry |
| topic | Fano 3-fold; Segre embedding; Gorenstein format |
| url | https://eprints.nottingham.ac.uk/45359/ https://eprints.nottingham.ac.uk/45359/ https://eprints.nottingham.ac.uk/45359/ |