Linearization of transition functions of a semi-positive line bundle along a certain submanifold

Let $X$ be a complex manifold and $L$ holomorphic line bundle on $X$. Assume that is semi-positive, namely admits smooth Hermitian metric with semi-positive Chern curvature. $Y$ compact K\"ahler submanifold of such the restriction to topologically trivial. We investigate obstruction for unitary flat neighborhood in As an application, example, we show existence nef, big, non non-singular projective surface.