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Geometric structures, the Gromov order, Kodaira dimensions and simplicial
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Neofytidis, Christoforos and Zhang, Weiyi (2021) Geometric structures, the Gromov order, Kodaira dimensions and simplicial. Pacific Journal of Mathematics, 315 (1). pp. 209-233. doi:10.2140/pjm.2021.315.209 ISSN 0030-8730.
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Official URL: https://doi.org/10.2140/pjm.2021.315.209
Abstract
We introduce an axiomatic definition for the Kodaira dimension and classify Thurston geometries in dimensions ≤5 in terms of this Kodaira dimension. We show that the Kodaira dimension is monotone with respect to the partial order defined by maps of nonzero degree between 5-manifolds. We study the compatibility of our definition with traditional notions of Kodaira dimension, especially the highest possible Kodaira dimension. To this end, we establish a connection between the simplicial volume and the holomorphic Kodaira dimension, which, in particular, implies that any smooth Kähler 3-fold with nonvanishing simplicial volume has top holomorphic Kodaira dimension.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Manifolds (Mathematics) , Kählerian manifolds, Complex manifolds | ||||||
| Journal or Publication Title: | Pacific Journal of Mathematics | ||||||
| Publisher: | Mathematical Sciences Publishers | ||||||
| ISSN: | 0030-8730 | ||||||
| Official Date: | 13 December 2021 | ||||||
| Dates: |
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| Volume: | 315 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 209-233 | ||||||
| DOI: | 10.2140/pjm.2021.315.209 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © Copyright 2021 Pacific Journal of Mathematics. All rights reserved. | ||||||
| Date of first compliant deposit: | 16 September 2021 | ||||||
| Date of first compliant Open Access: | 19 January 2022 | ||||||
| Related URLs: |
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