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ISSN 1088-6850(e) ISSN 0002-9947(p)

Sharp bounds on Castelnuovo-Mumford regularity

Author(s): Chikashi Miyazaki
Journal: Trans. Amer. Math. Soc. 352 (2000), 1675-1686.
MSC (1991): Primary 14B15; Secondary 13D45, 13H10, 14M05
Posted: 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 , $\operatorname{reg}(X)\le\lceil(\deg (X) - 1)/\operatorname{codim}(X)\rceil +k \cdot \dim (X)$ , provided is -Buchsbaum for $k \ge 1$ , and investigate the projective variety with its Castelnuovo-Mumford regularity having such an upper bound.

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