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arXiv · 2508.17237

Remark on semi-positive holomorphic sectional curvature and quasi-negative $k$-Ricci curvature

Shiyu Zhang
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Abstract

We record two remarks. First, for a compact Kähler manifold with semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration is exactly the number of non-truly-flat directions. Second, for compact Kähler manifolds with quasi-negative $k$-Ricci curvature, $1 0$, the canonical bundle is ample.

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Shiyu Zhang. 2026-05-28. Remark on semi-positive holomorphic sectional curvature and quasi-negative $k$-Ricci curvature. https://arxiv.org/abs/2508.17237

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