2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/267The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.105 pages. Minor typos correctedAlgebraic Geometry14E05, 14E30, 14J25, 14J30text