Sharp bounds on Castelnuovo-Mumford regularity

Miyazaki, Chikashi

doi:10.1090/S0002-9947-99-02380-6

Sharp bounds on Castelnuovo-Mumford regularity
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by Chikashi Miyazaki PDF

Trans. Amer. Math. Soc. 352 (2000), 1675-1686 Request permission

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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