2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137891Let X be a smooth projective variety and let K be the canonical divisor of X. In this paper, we study embeddings of X given by adjoint line bundles of the form K+L, where L is an ample line bundle. When X is a regular surface (i.e. H^1(X, O_X) = 0), we obtain a numerical criterion for K+L to have property Np. When X is a regular variety of arbitrary dimension, under a mild condition, we give an explicit calculation for the regularity of the ideal sheaves of such embeddings.15 pages; fix a mistake in Lemma 3.5; final versionAlgebraic GeometryCommutative Algebra14F17, 13D02, 14J60, 14C20text