Arithmetically buchsbaum divisors on varieties of minimal degree

In this paper we consider integral arithmetically Buchsbaum subschemes of projective space. First we show that arithmetical Buclisbaum varieties of sufficiently large degree have maximal Castelnuovo-Mumford regularity if and only if they are divisors on a variety of minimal degree. Second we determine all varieties of minimal degree and their divisor classes which contain an integral arithmetically Buchsbaum subscheme. Third we investigate these varieties. In particular, we compute their Hilbert function, cohomology modules and (often) their graded Betti numbers and obtain an existence result for smooth arithmetically Buchsbaum varieties.