Abstract
For an effective divisor $A$ with support $B$ in a compact Kähler manifold $M$ of dimension $\geq 3$, the following are antinomic.
a) $M\backslash B$ has a $C^{\infty}$ plurisubharmonic exhaustion function whose Levi form has pointwise at least 3 positive eigenvalues outside a compact subset of $M\backslash B$.
b) $[A]|B$, the normal bundle of $A$, is topologically trivial.
Citation
Takeo Ohsawa. "A remark on pseudoconvex domains with analytic complements in compact Kähler manifolds." J. Math. Kyoto Univ. 47 (1) 115 - 119, 2007. https://doi.org/10.1215/kjm/1250281070
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