Abstract
We show that if a compact complex manifold admits a Kähler metric whose holomorphic sectional curvature is everywhere non-positive and strictly negative in at least one point, then its canonical bundle is positive. This answers in the affirmative to a question first asked by S.-T. Yau.
Funding Statement
The first-named author is partially supported by the ANR Programme: Défi de tous les savoirs (DS10) 2015, “GRACK”, Project ID: ANR-15-CE40-0003ANR, and Défi de tous les savoirs (DS10) 2016, “FOLIAGE”, Project ID: ANR-16-CE40-0008.
Citation
Simone Diverio. Stefano Trapani. "Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle." J. Differential Geom. 111 (2) 303 - 314, February 2019. https://doi.org/10.4310/jdg/1549422103
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