2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58487We develop an intersection theory for a singular hemitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure associated with the singular hermitian line bundle. Also for any pseudoeffective line bundle on a smooth projective variety, we prove the existence of a rational natural fibration structure associated with the line bundle. We also characterize a numerically trivial singular hermitain line bundle on a smooth projective variety.Algebraic Geometry32J25text