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Intersection of almost complex submanifolds
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Zhang, Weiyi (2018) Intersection of almost complex submanifolds. Cambridge Journal of Mathematics, 6 (4). pp. 451-496. doi:10.4310/CJM.2018.v6.n4.a2 ISSN 2168-0930.
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Official URL: https://doi.org/10.4310/CJM.2018.v6.n4.a2
Abstract
We show the intersection of a compact almost complex sub- variety of dimension 4 and a compact almost complex submanifold of codimension 2 is a J -holomorphic curve. This is a generalization of positivity of intersections for J -holomorphic curves in almost complex 4-manifolds to higher dimensions. As an application, we discuss pseudo- holomorphic sections of a complex line bundle. We introduce a method to produce J-holomorphic curves using the differential geometry of almost Hermitian manifolds. When our main result is applied to pseudoholomorphic maps, we prove the singularity subset of a pseudoholomorphic map between almost complex 4-manifolds is J -holomorphic. Building on this, we show degree one pseudoholomorphic maps between almost complex 4-manifolds are actually birational morphisms in pseudoholomorphic category.
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): | Submanifolds, Holomorphic functions | ||||||
Journal or Publication Title: | Cambridge Journal of Mathematics | ||||||
Publisher: | International Press | ||||||
ISSN: | 2168-0930 | ||||||
Official Date: | 23 October 2018 | ||||||
Dates: |
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Volume: | 6 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 451-496 | ||||||
DOI: | 10.4310/CJM.2018.v6.n4.a2 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 15 August 2018 | ||||||
Date of first compliant Open Access: | 15 August 2018 | ||||||
RIOXX Funder/Project Grant: |
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