Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Sharp bounds on
Castelnuovo-Mumford regularity

Author: Chikashi Miyazaki
Journal: Trans. Amer. Math. Soc. 352 (2000), 1675-1686
MSC (1991): Primary 14B15; Secondary 13D45, 13H10, 14M05
Published electronically: October 21, 1999
MathSciNet review: 1621769
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Abstract: The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic measures such as dimension, codimension and degree. In this paper we consider an upper bound on the regularity $\operatorname{reg}(X)$ of a nondegenerate projective variety $X$, $\operatorname{reg}(X)\le\lceil(\deg (X) - 1)/\operatorname{codim}(X)\rceil +k \cdot \dim (X)$, provided $X$ is $k$-Buchsbaum for $k \ge 1$, and investigate the projective variety with its Castelnuovo-Mumford regularity having such an upper bound.

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Additional Information

Chikashi Miyazaki
Affiliation: Department of Mathematical Sciences, University of the Ryukyus, Nishihara-cho, Okinawa 903-0213, Japan

Received by editor(s): July 15, 1997
Received by editor(s) in revised form: February 28, 1998
Published electronically: October 21, 1999
Additional Notes: Partially supported by Grant-in-Aid for Scientific Research (no. 09740042), Ministry of Education, Science, Sports and Culture, Japan
Article copyright: © Copyright 2000 American Mathematical Society