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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
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Official URL: https://doi.org/10.1007/s40879-017-0200-2
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 | ||||||||||||
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| 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: |
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| 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 | ||||||||||||
| Description: | Please see publisher's version for correctly formatted formulae. |
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