“…Indeed, as it follows from [CLPT,Proposition 2.7] that the fibration as in the theorem exists if the natural map H 1 (X, O X ) → H 1 (Y, O Y ) is not injective. Therefore it is sufficient to consider the case where Pic As N m Y /X is not holomorphically trivial for any positive integer m, one has that, for any neighborhood Ω of Y , there exists a compact Levi-flat hypersurface H in Ω \ Y such that each leaf of the Levi foliation of H is dense in H. Then it holds that any holomorphic function on Ω \ Y is constant (see the proof of [KU,Lemma 2.2] for example). Therefore it is clear that the Hartogs type extension theorem holds on X \ Y .…”