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Kodaira dimensions of almost complex manifolds II
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Chen, Haojie and Zhang, Weiyi (2024) Kodaira dimensions of almost complex manifolds II. Communications in Analysis and Geometry . ISSN 1019-8385. (In Press)
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Abstract
This is the second of a series of papers where we study the plurigen- era, the Kodaira dimension and the Iitaka dimension on compact almost complex manifolds. By using the pseudoholomorphic pluricanonical map, we define the second version of Kodaira dimension as well as Iitaka dimension on compact almost complex manifolds. We show that almost complex structures with the top Kodaira dimension are integrable. For compact almost complex 4-manifolds with Kodaira dimension one, we obtain elliptic fibration like structural descrip- tion. Some vanishing theorems in complex geometry are generalized to the almost complex setting. For tamed symplectic 4-manifolds, we show that the almost Kodaira dimension is bounded above by the symplectic Kodaira dimension, by using a probabilistic combinatorics style argument. The appendix also contains a few results including answering a question of the second author that there is a unique subvariety in ex- ceptional curve classes for irrational symplectic 4-manifolds, as well as extending Evans-Smith’s constraint on symplectic embeddings of certain rational homology balls by removing the assumption on the intersection form.
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): | Almost complex manifolds , Geometry, Geodesic flows, Pseudoholomorphic curves | ||||||
Journal or Publication Title: | Communications in Analysis and Geometry | ||||||
Publisher: | International Press | ||||||
ISSN: | 1019-8385 | ||||||
Official Date: | 2024 | ||||||
Dates: |
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Status: | Peer Reviewed | ||||||
Publication Status: | In Press | ||||||
Re-use Statement: | © by International Press of Boston, Inc. All rights reserved. | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 17 March 2022 | ||||||
Date of first compliant Open Access: | 18 March 2022 | ||||||
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