  Ueda's theory is a theory on a flatness criterion around a smooth
hypersurface of a certain type of topologically trivial holomorphic line
bundles. We propose a codimension two analogue of Ueda's theory. As an
application, we give a sufficient condition for the anti-canonical bundle of
the blow-up of the three dimensional projective space at $8$ points to be non
semi-ample however admit a smooth Hermitian metric with semi-positive
curvature.
