Reduction of manifolds with semi-negative holomorphic sectional curvature

Gordon Heier; Steven S. Y. Lu; Bun Wong; Fangyang Zheng

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arXiv · 1705.00605

Reduction of manifolds with semi-negative holomorphic sectional curvature

Gordon Heier·Steven S. Y. Lu·Bun Wong·Fangyang Zheng

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Abstract

In this note, we continue the investigation of a projective K\"ahler 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 {\it 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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BibTeX RIS

Gordon Heier, Steven S. Y. Lu, Bun Wong, Fangyang Zheng. 2017-05-01. Reduction of manifolds with semi-negative holomorphic sectional curvature. https://arxiv.org/abs/1705.00605

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