Asymptotic Behaviour of the Castelnuovo-Mumford Regularity
Asymptotic Behaviour of the Castelnuovo-Mumford Regularity
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DOI：
10.1023/a:1001559912258
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发表时间：
1999-09
影响因子：
1.8
通讯作者：
S. Cutkosky;J. Herzog;Ngô Viêt Trung
中科院分区：
文献类型：
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作者：
S. Cutkosky;J. Herzog;Ngô Viêt Trung
本文研究了齐次理想I的方幂的Castelnuovo Mumford正则性的渐近性态。证明了以I的齐次生成元的最大次数为斜率的幂I的正则性存在一个线性界，并且当n较大时，I的正则性是一个线性函数.类似的结果也适用于I的幂的积分闭包。另一方面，我们给出了饱和幂的正则性渐近地不是线性函数，甚至不是具有周期系数的线性函数的理想的例子。
In this paper the asymptotic behavior of the Castelnuovo$ndash;Mumford regularity of powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the regularity of the powers I whose slope is the maximum degree of a homogeneous generator of I, and that the regularity of I is a linear function for large n. Similar results hold for the integral closures of the powers of I. On the other hand we give examples of ideal for which the regularity of the saturated powers is asymptotically not a linear function, not even a linear function with periodic coefficients.