2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165349In this article we prove a non-vanishing statement, as well as several properties of metrics with minimal singularities of adjoint bundles. Our arguments involve many ideas from Y.-T. Siu's analytic proof of the finite generation of the canonical ring. An important technical tool is the notion of relative critical exponent of two closed positive currents with respect to a measure.No figuresComplex VariablesAlgebraic Geometrytext