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The curve cone of almost complex 4-manifolds
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Zhang, Weiyi (2017) The curve cone of almost complex 4-manifolds. Proceedings of the London Mathematical Society, 115 (6). pp. 1227-1275. doi:10.1112/plms.12062 ISSN 0024-6115 .
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Official URL: https://doi.org/10.1112/plms.12062
Abstract
In this paper, we study the curve cone of an almost complex 4‐manifold which is tamed by a symplectic form. In particular, we prove the cone theorem as in Mori theory for all such manifolds using the Seiberg–Witten theory. For small rational surfaces and minimal ruled surfaces, we study the configuration of negative curves. We define abstract configuration of negative curves, which records the homological and intersection information of curves. Combinatorial blowdown is the main tool to study these configurations. As an application of our investigation of the curve cone, we prove the Nakai–Moishezon type duality for all almost Kähler structures on ℂ
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Proceedings of the London Mathematical Society | ||||||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||
ISSN: | 0024-6115 | ||||||||
Official Date: | December 2017 | ||||||||
Dates: |
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Volume: | 115 | ||||||||
Number: | 6 | ||||||||
Page Range: | pp. 1227-1275 | ||||||||
DOI: | 10.1112/plms.12062 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 27 July 2017 | ||||||||
Date of first compliant Open Access: | 6 March 2018 | ||||||||
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