Let $C$ be a compact complex curve included in a non-singular complex
surface such that the normal bundle is topologically trivial.
Ueda studied complex analytic properties of a neighborhood of $C$ when
$C$ is non-singular or is a rational curve with a node. We propose a
codimension two analogue of Ueda's theory. As an application, we study
singular Hermitian metrics with semi-positive curvature on the blow-up
of the three dimensional projective space at 8 points.


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