Arithmetically Buchsbaum divisors on varieties of minimal degree

In this paper we consider integral arithmetically Buchsbaum subschemes of p rojective space. First we show that arithmetical Buchsbaum varieties of suf ficiently large degree have maximal Castelnuovo-Mumford regularity if and o nly if they are divisors on a variety of minimal degree. Second we determin e all varieties of minimal degree and their divisor classes which contain a n integral arithmetically Buchsbaum subscheme. Third we investigate these v arieties. In particular, we compute their Hilbert function, cohomology modu les and (often) their graded Betti numbers and obtain an existence result f or smooth arithmetically Buchsbaum varieties.