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Geometric structures,
the Gromov order, Kodaira dimensions and simplicial
volume
Christoforos Neofytidis and Weiyi Zhang |
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Vol. 315 (2021), No. 1, 209–233
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Abstract |
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We introduce an axiomatic definition for the Kodaira dimension and classify Thurston geometries in dimensions 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 -fold with nonvanishing simplicial volume has top holomorphic Kodaira dimension. |
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Keywords
Kodaira dimension, Thurston geometry, simplicial volume,
nonzero degree, Gromov's order, 5-manifold, projective
manifold, Kähler manifold
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Mathematical Subject Classification
Primary: 57M50, 57N16
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Milestones
Received: 25 January 2021
Revised: 4 July 2021
Accepted: 13 September 2021
Published: 13 December 2021
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Authors |
| Christoforos Neofytidis | |
| Department of Mathematics Ohio State University Columbus, OH United States |
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| Weiyi Zhang | |
| Mathematics Institute University of Warwick Coventry United Kingdom |
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