2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69036We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of multiplicity $(s-2)$. This implies that $S$ contains a plane curve. We prove that the degree of such surfaces is bounded and for $s=4$ we compute an actual bound.10 pages. The content has been replaced since there was an error in the proof of the main theoremAlgebraic Geometry14J10text