2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69254In this paper the log surfaces without $\QQ$-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows one to apply it in the most wide class of log surfaces.Latex2e, 3 pagesAlgebraic Geometrytext