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


Author: Chikashi Miyazaki
Journal: Proc. Amer. Math. Soc. 139 (2011), 1909-1914
MSC (2010): Primary 13H10, 14M05; Secondary 14N25
DOI: https://doi.org/10.1090/S0002-9939-2011-10920-1
Published electronically: February 1, 2011
MathSciNet review: 2775367
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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)/ {\mbox{\rm 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)/ {\mbox{\rm codim} } V \rceil$ is a divisor on a Del Pezzo variety if $ \deg V \gg 0$.


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Additional Information

Chikashi Miyazaki
Affiliation: Department of Mathematics, Saga University, Honjo-machi 1, Saga 840-8502, Japan
Email: miyazaki@ ms.saga-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2011-10920-1
Keywords: Castelnuovo-Mumford regularity, Buchsbaum ring, Rational normal scroll, Del Pezzo variety
Received by editor(s): May 18, 2009
Received by editor(s) in revised form: March 12, 2010, and March 25, 2010
Published electronically: February 1, 2011
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C) (21540044) Japan Society for the Promotion of Science
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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