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

This paper is devoted to the study of the next extremal case for a Castelnuovo-type bound $ \mathrm{reg} V \le \lceil (\deg V - 1)/ {\mbox{\rm codim} } V \rceil + 1$. 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 $ \mathrm{reg} V = \lceil (\deg V - 1)/ {\mbox{\rm codim} } V \rceil$ $ \deg V \gg 0$ [ABSTRACT FROM AUTHOR]