2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76632We prove that the bicanonical system on a surface of general type with K^2=4 has no base components and describe clusters contracted by 4K_X for a numerical Godeaux surface and 3K_X for a numerical Campedelli surface.10 pages in AMS-TeXAlgebraic Geometrytext