## Journal of Mathematics of Kyoto University

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

Takeo Ohsawa

#### 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.

#### Article information

Source
J. Math. Kyoto Univ., Volume 47, Number 1 (2007), 115-119.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281070

Digital Object Identifier
doi:10.1215/kjm/1250281070

Mathematical Reviews number (MathSciNet)
MR2359103

Zentralblatt MATH identifier
1151.32006

#### Citation

Ohsawa, Takeo. A remark on pseudoconvex domains with analytic complements in compact Kähler manifolds. J. Math. Kyoto Univ. 47 (2007), no. 1, 115--119. doi:10.1215/kjm/1250281070. https://projecteuclid.org/euclid.kjm/1250281070