Work

Quasi‐positive mixed curvature, vanishing theorems, and rational connectedness

Year: 2026

Type: article

Abstract: In this paper, we consider mixed curvature , which is a convex combination of Ricci curvature and holomorphic sectional curvature introduced by Chu–Lee–Tam [Trans. Amer. Math. Soc. 375 (2022), no. 11, 7925‐7944]. We prove that if a compact complex manifold admits a Kähler metric with quasi‐positive mixed curvature and , then it is projective. If , then is rationally connected. As a corollary, the same result holds for ‐Ricci curvature. We also show that any compact Kähler manifold with quasi‐positive 2‐scalar curvature is projective. Lastly, we generalize the result to the Hermitian case. In particular, any compact Hermitian threefold with quasi‐positive real bisectional curvature has vanishing Hodge number . Furthermore, if it is Kählerian, then it is projective.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70294

Author: Kai Tang

Institution: Zhejiang Normal University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province

Awards: 混合曲率的若干几何问题, G950083780