Stability of Pseudo-Kähler Manifolds and Cohomological Decomposition

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 b1,1BC(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