A remark on pseudoconvex domains with analytic complements in compact Kähler manifolds

For an effective divisor A with support B in a compact K¨ahler manifold M of dimension ≥ 3, the following are antinomic. a) M \ B has a C ∞ plurisubharmonic exhaustion function whose Levi form has pointwise at least 3 positive eigenvalues outside a compact subset of M \ B . b) [ A ] | B , the normal bundle of A , is topologically trivial.