Proper Modifications of Generalized p-Kähler Manifolds

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In this paper, we consider a proper modification $$f : \tilde{M} \rightarrow M$$ between complex manifolds, and study when a generalized p-Kahler property goes back from M to $$\tilde{M}$$ . When f is the blow-up at a point, every generalized p-Kahler property is conserved, while when f is the blow-up along a submanifold, the same is true for $$p=1$$ . For $$p=n-1$$ , we prove that the class of compact generalized balanced manifolds is closed with respect to modifications, and we show that the fundamental forms can be chosen in the expected cohomology class. We also get some partial results in the non-compact case; finally, we end the paper with some examples of generalized p-Kahler manifolds.