We study here Kähler-type properties of 1-convex manifolds, using the duality between forms and compactly supported currents, and some properties of the Aeppli groups of q-convex manifolds. We prove that, when the exceptional set S of the 1-convex manifold X has dimension k, X is p-Kähler for every p > k, and is k-Kähler if and only if "the fundamental class" of S does not vanish. There are classical examples where X is not k-Kähler even with a smooth S, but we prove that this cannot happen if 2k ≥ n = dim X, nor for suitable neighborhoods of S; in particular, X is always balanced (i.e., (n - 1)-Kähler).
1-convex manifolds are p-Kähler / ALESSANDRINI L.; BASSANELLI G.; LEONI M.. - In: ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG. - ISSN 0025-5858. - 72(2002), pp. 255-268. [10.1007/BF02941676]