A general Schwarz lemma for Hermitian manifolds
Abstract
Abstract We prove a general Schwarz lemma for holomorphic maps between Hermitian manifolds. As a consequence, we show that a compact Kähler manifold with a pluriclosed metric of negative holomorphic sectional curvature is canonically polarized. In particular, such manifolds are projective and admit a Kähler–Einstein metric with negative scalar curvature.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN