Gorenstein liaison of divisors on standard determinantal schemes and on rational normal scrolls

Let image be an arithmetically Cohen–Macaulay subscheme. In terms of Gorenstein liaison it is natural to ask whether C is in the Gorenstein liaison class of a complete intersection. In this paper, we study the Gorenstein liaison classes of arithmetically Cohen–Macaulay divisors on standard determinantal schemes and on rational normal scrolls. As main results, we obtain that if C is an arithmetically Cohen–Macaulay divisor on a “general” arithmetically Cohen–Macaulay surface in image or on a rational normal scroll surface image, then C is glicci (i.e. it belongs to the Gorenstein liaison class of a complete intersection).