Abstract
In this note, we continue the investigation of a projective Kähler manifold M of semi-negative holomorphic sectional curvature H. We introduce a new differential geometric numerical rank invariant which measures the number of linearly independent truly flat directions of H in the tangent spaces. We prove that this invariant is bounded above by the nef dimension and bounded below by the numerical Kodaira dimension of M. We also prove a splitting theorem for M in terms of the nef dimension and, under some additional hypotheses, in terms of the new rank invariant.
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Acknowledgements
We would like to thank Kefeng Liu, Hongwei Xu, and Shing-Tung Yau for their interest.
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F. Zheng is partially supported by a Simons Collaboration Grant.
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Heier, G., Lu, S.S.Y., Wong, B. et al. Reduction of manifolds with semi-negative holomorphic sectional curvature. Math. Ann. 372, 951–962 (2018). https://doi.org/10.1007/s00208-017-1638-8
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DOI: https://doi.org/10.1007/s00208-017-1638-8