Dolbeault and Bott-Chern formalities: deformations and $\partial\overline{\partial}$-lemma
Dolbeault and Bott-Chern formalities: deformations and $\partial\overline{\partial}$-lemma
It is proved that the properties of being Dolbeault formal and geometrically-Bott-Chern-formal are not closed under holomorphic deformations of the complex structure. Further, we construct a compact complex manifold which satisfies the $\partial\overline{\partial}$-lemma but admits a non vanishing Aeppli-Bott-Chern-Massey product.
Mathematics - Differential Geometry, Complex manifolds, Differential Geometry (math.DG), deformations of the complex structure, FOS: Mathematics, Deformations of complex structures, 32Q99, 32S45, 32G05, Modifications; resolution of singularities (complex-analytic aspects), \(\partial \overline{\partial}\)-lemma
Mathematics - Differential Geometry, Complex manifolds, Differential Geometry (math.DG), deformations of the complex structure, FOS: Mathematics, Deformations of complex structures, 32Q99, 32S45, 32G05, Modifications; resolution of singularities (complex-analytic aspects), \(\partial \overline{\partial}\)-lemma
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