2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68362In this paper we compute the Hilbert functions of irreducible (or smooth) and reduced arithmetically Gorenstein schemes that are twisted anti-canonical divisors on arithmetically Cohen-Macaulay schemes. We also prove some folklore results characterizing the Hilbert functions of irreducible standard determinantal schemes, and we use them to produce a new class of functions that occur as Hilbert functions of irreducible (or smooth) and reduced arithmetically Gorenstein schemes in any codimension.17 pages, to appear in Journal of AlgebraAlgebraic GeometryCommutative Algebra14M05text