2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62139We prove that the irregularity of a smooth abelian scroll whose dimension is at least half of that of the surrounding projective space is bounded by 2. In addition we discuss some existence results and open problems.8 pages, Latex 2e, to appear in Festschrift in honour of Hans GrauertAlgebraic GeometryA bound on the irregularity of abelian scrolls in projective spacetext