$(\varepsilon, \delta)$--Quasi-Negative Curvature and Positivity of the Canonical Bundle

DOI10.1007/S12220-024-01619-4arXiv2305.01881OpenAlexW4394843708MaRDI QIDQ6435129

Kai Tang, Kyle Broder

Publication date: 3 May 2023

Abstract: A recent theorem of Diverio--Trapani and Wu--Yau asserts that a compact K"ahler manifold with a K"ahler metric of quasi-negative holomorphic sectional curvature is projective and canonically polarized. This confirms a long-standing conjecture of Yau. We consider the notion of $(varepsilon,delta)$--quasi-negativity, generalizing quasi-negativity, and obtain gap-type theorems for $in{t}_X{c}_1(K_X{)}^n>0$ in terms of the real bisectional curvature and weighted orthogonal Ricci curvature. These theorems are also a generalization of that results in cite{ZhangZheng} by Zhang-Zheng and in cite{ChuLeeTam} by Chu-Lee-Tam.

Full work available at URL: https://doi.org/10.1007/s12220-024-01619-4

Mathematics Subject Classification ID

Several complex variables and analytic spaces (32-XX)

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