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arXiv · 2607.18778

The spaces of K\"ahler and holomorphically tamed symplectic forms on closed 4-manifolds

Tian-Jun Li·Shengzhen Ning
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Abstract

This paper investigates the uniqueness, connectedness and openness properties of spaces of K\"ahler forms on closed $4$-manifolds, extending discussions in \cite{Li08,Sal13}. Motivated by the Streets--Tian conjecture concerning the existence of K\"ahler metrics on Hermitian-symplectic complex manifolds, we also study holomorphically tamed symplectic forms, which are symplectic forms tamed by some integrable complex structure. We formulate a parallel question and relate it to the corresponding questions for K\"ahler-type symplectic forms.

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BibTeXRIS

Tian-Jun Li, Shengzhen Ning. 2026-07-21. The spaces of K\"ahler and holomorphically tamed symplectic forms on closed 4-manifolds. https://arxiv.org/abs/2607.18778

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