2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79458We use the geometry of the secant variety to an embedded smooth curve to prove some vanishing and regularity theorems for powers of ideal sheaves.14 pages, LaTeX2e; Streamlined, some references added; to appear in Comp. MathAlgebraic Geometry14F17;14H60;14N05text