Abstract:We consider compact complex manifolds endowed with a pseudo-Kähler structure and study their stability under deformations. It is known that if the Bott-Chern number b 1,1 BC (Xt) is constant along a deformation Xt whose central fiber X0 is pseudo-Kähler, then Xt also admits a pseudo-Kähler structure, at least for sufficiently small t. Here we find another condition for stability related to the cohomological decomposition of complex manifolds.
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