The spaces of Kähler and holomorphically tamed symplectic forms on closed 4-manifolds

2026/07/21 by Tian-Jun Li, Shengzhen Ning · 1 voice
#math.SG #math.AG #math.DG

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Abstract

This paper investigates the uniqueness, connectedness and openness properties of spaces of Kähler forms on closed 4-manifolds, extending discussions in \citeLi08,Sal13. Motivated by the Streets--Tian conjecture concerning the existence of Kähler 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 Kähler-type symplectic forms.

Discussions

• Tian-Jun Li, Shengzhen Ning: The spaces of K\"ahler and holomorphically tamed symplectic forms on closed 4-manifolds https://arxiv.org/abs/2607.18778 https://arxiv.org/pdf/2607.18778 https://arxiv.org [bsky, 0 points, 0 comments]

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