Buchsbaum varieties with next to sharp bounds on Castelnuovo-Mumford regularity

Abstract

This paper is devoted to the study of the next extremal case for a Castelnuovo-type bound regV ≤ ?(deg V―1)/codim V?+1 of the Castelnuovo-Mumford regularity for a nondegenerate Buchsbaum variety V. A Buchsbaum variety with the maximal regularity is known to be a divisor on a variety of minimal degree if the degree of the variety is large enough. We show that a Buchsbaum variety satisfying regV = ?(deg V — 1)/codim V? is a divisor on a Del Pezzo variety if deg V ≫ 0.