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A holomorphic line bundle over a compact complex manifold is shown to be big if it has a singular Hermitian metric whose curvature current is smooth on the complement of some proper analytic subset, strictly positive on some tubular neighborhood of the analytic subset, and satisfies a condition on its integral. In particular, we obtain a sufficient condition for a compact complex manifold to be a Moishezon space.

A differential geometric property of big line bundles