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arXiv · 2008.00592

Geometric structures, the Gromov order, Kodaira dimensions and simplicial volume

Christoforos Neofytidis·Weiyi Zhang
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Abstract

We introduce an axiomatic definition for the Kodaira dimension and classify Thurston geometries in dimensions $\leq 5$ in terms of this Kodaira dimension. We show that the Kodaira dimension is monotone with respect to the partial order defined by maps of non-zero 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 non-vanishing simplicial volume has top holomorphic Kodaira dimension.

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Christoforos Neofytidis, Weiyi Zhang. 2021-09-15. Geometric structures, the Gromov order, Kodaira dimensions and simplicial volume. https://doi.org/10.2140/pjm.2021.315.209

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