This research proves a Schwarz lemma for holomorphic maps in Hermitian manifolds, suggesting implications for their polarization.
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.
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Broder et al. (2026) studied this question.
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