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J-Holomorphic curves in a Nef class
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Li, T. -J. and Zhang, W. (2015) J-Holomorphic curves in a Nef class. International Mathematics Research Notices, 2015 (22). pp. 12070-12104. doi:10.1093/imrn/rnv056 ISSN 1073-7928.
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WRAP-J−HOLOMORPHIC-CURVES-CLASS-Zhang-2019.pdf - Accepted Version - Requires a PDF viewer. Download (854Kb) | Preview |
Official URL: http://dx.doi.org/10.1093/imrn/rnv056
Abstract
Taubes established fundamental properties of J-holomorphic subvarieties in dimension 4 in [8]. In this paper, we further investigate properties of reducible J-holomorphic subvarieties. We offer an upper bound of the total genus of a subvariety when the class of the subvariety is J-nef. For a spherical class, it has particularly strong consequences. It is shown that, for any tamed J, each irreducible component is a smooth rational curve. It might be even new when J is integrable. We also completely classify configurations of maximal dimension. To prove these results, we treat subvarieties as weighted graphs and introduce several combinatorial moves.
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): | Holomorphic functions, Combinatorial analysis , Hausdorff measures | ||||||
Journal or Publication Title: | International Mathematics Research Notices | ||||||
Publisher: | Oxford University Press | ||||||
ISSN: | 1073-7928 | ||||||
Official Date: | 9 March 2015 | ||||||
Dates: |
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Volume: | 2015 | ||||||
Number: | 22 | ||||||
Page Range: | pp. 12070-12104 | ||||||
DOI: | 10.1093/imrn/rnv056 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in, International Mathematics Research Notices following peer review. The version of record Tian-Jun Li, Weiyi Zhang, J-Holomorphic Curves in a Nef Class, International Mathematics Research Notices, Volume 2015, Issue 22, 2015, Pages 12070–12104 is available online at: https://doi.org/10.1093/imrn/rnv056. | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 30 October 2019 | ||||||
Date of first compliant Open Access: | 30 October 2019 |
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