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Characterizes the ∂∂¯-lemma in twistor spaces and computes Dolbeault cohomology in a specific setting, indicating important properties of these mathematical structures.
In the paper we study the Bott-Chern and Aeppli cohomologies of the twistor space of a compact self-dual 4-manifold and we characterize the validity of the ∂ ∂ ¯ -lemma. We also compute explicitly the Dolbeault cohomology of the twistor space Z of the flat 4-dimensional torus, which is known to not satisfy the ∂ ∂ ¯ lemma.
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Fino et al. (2026) studied this question.
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