Hodge symmetry holds for smoothings of SNC varieties without triple points when monodromy induces graded isomorphisms on limiting mixed Hodge structures; Hodge-Riemann relations hold on H^3 for such 3-folds under additional conditions.
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On Hodge structures of compact complex manifolds with semistable degenerations
Hodge symmetry holds for smoothings of SNC varieties without triple points when monodromy induces graded isomorphisms on limiting mixed Hodge structures; Hodge-Riemann relations hold on H^3 for such 3-folds under additional conditions.