Q-Complete domains with corners in {mathbb{P}^n} and extension of line bundles

We show that if a compact set X in ${mathbb P^n}$ is laminated by holomorphic submanifolds of dimension q, then ${mathbb P^n{setminus}X}$ is (q + 1)-complete with corners. Consider a manifold U, q-complete with corners. Let ${mathcal N}$ be a holomorphic line bundle in the complement of a compact in U. We study when ${mathcal N}$ extends as a holomorphic line bundle in U. We give applications to the non existence of some Levi-flat foliations in open sets in ${mathbb P^n}$ . The results apply in particular when U is a Stein manifold of dimension n ≥ 3, then every holomorphic line bundle in the complement of a compact extends holomorphically to U.