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Harmonic forms on the Kodaira-Thurston manifold
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Holt, Thomas and Zhang, Weiyi (2022) Harmonic forms on the Kodaira-Thurston manifold. Advances in Mathematics, 400 . 108277. doi:10.1016/j.aim.2022.108277 ISSN 0001-8708.
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Official URL: http://doi.org/10.1016/j.aim.2022.108277
Abstract
We introduce an effective method to determine the -harmonic forms on the Kodaira-Thurston manifold endowed with an almost complex structure and an almost Hermitian metric. Using the Weil-Brezin transform, we reduce the elliptic PDE system to countably many linear ODE systems. By solving a fundamental problem on linear ODE systems, the problem of finding -harmonic forms is equivalent to a generalised Gauss circle problem.
We demonstrate two remarkable applications. First, the dimension of the almost complex -Hodge numbers on the Kodaira-Thurston manifold could be arbitrarily large. Second, Hodge numbers vary with different choices of almost Hermitian metrics. This answers a question of Kodaira and Spencer in Hirzebruch's 1954 problem list.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Advances in Mathematics | ||||||||
Publisher: | Academic Press | ||||||||
ISSN: | 0001-8708 | ||||||||
Official Date: | 14 May 2022 | ||||||||
Dates: |
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Volume: | 400 | ||||||||
Article Number: | 108277 | ||||||||
DOI: | 10.1016/j.aim.2022.108277 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 24 February 2022 | ||||||||
Date of first compliant Open Access: | 23 February 2023 | ||||||||
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