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

Miyazaki, Chikashi

doi:10.1090/S0002-9939-2011-10920-1

Buchsbaum varieties with next to sharp bounds on Castelnuovo-Mumford regularity
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Proc. Amer. Math. Soc. 139 (2011), 1909-1914 Request permission

Abstract:

This paper is devoted to the study of the next extremal case for a Castelnuovo-type bound $\mathrm {reg} V \le \lceil (\deg V - 1)/ \operatorname {codim} V \rceil + 1$ 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 $\mathrm {reg} V = \lceil (\deg V - 1)/ \operatorname {codim} V \rceil$ is a divisor on a Del Pezzo variety if $\deg V \gg 0$.

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