We investigate the canonical bundle and Kodaira dimension of nearly Kähler 6-manifolds. We prove that the canonical bundle of a strictly nearly Kähler 6-manifold is pseudoholomorphically trivial. Therefore, the Kodaira dimension is zero. As a corollary, we show the existence of non-integrable almost complex structure on CP3 whose Kodaira dimension is not -∞. We also construct explicit generating sections of the canonical bundle of homogeneous strictly nearly Kähler 6-manifolds and prove that the Hodge numbers h1,0, h2,0, h2,3, h1,3 of the homogeneous strictly nearly Kähler F3 and CP3 are all zeros.
Hao Jie CHEN, Guan Ming WANG.
Kodaira Dimension of Nearly Kähler 6-manifolds. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 87-98 https://doi.org/10.12386/A2021sxxb0007
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