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Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links
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Blanc, J. and Lamy, Stephane (2012) Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links. Proceedings of the London Mathematical Society, Volume 105 (Number 5). pp. 1047-1075. doi:10.1112/plms/pds023 ISSN 0024-6115 .
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Official URL: http://dx.doi.org/10.1112/plms/pds023
Abstract
We characterize smooth curves in ℙ3 whose blow-up produces a threefold with anticanonical divisor big and nef. These are curves C of degree d and genus g lying on a smooth quartic, such that (i) 4d−30≤g≤14 or (g, d)=(19, 12), (ii) there is no 5-secant line, 9-secant conic nor 13-secant twisted cubic to C. This generalizes the classical similar situation for the blow-up of points in ℙ2.
We describe then Sarkisov links constructed from these blow-ups, and are able to prove the existence of Sarkisov links which were previously only known as numerical possibilities.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Proceedings of the London Mathematical Society | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0024-6115 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Volume 105 | ||||
Number: | Number 5 | ||||
Page Range: | pp. 1047-1075 | ||||
DOI: | 10.1112/plms/pds023 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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