理想幂的正则亏损稳定性
Regularity defect stabilization of powers of an ideal
摘要：
当I是具有齐次极大理想\mm的标准分次代数S的理想时，由几位作者的工作可知，I^m的Castelnuovo-Mumford正则性最终成为m \gg 0的线性函数dm + e。我们给出了几个关于可称为\emph{regularity defect}（序列e_m = \reg I^m-dm）的行为的约束。当I是\mm -primary时，我们给出了e_m的第一个差的一个界族，包括序列的增加部分的上界;例如，我们证明了e_i对于i \geq \dim（S）不能增加。当I是单项式理想时，我们证明了对于i \geq n（n-1）（d-1），其中n = \dim（S），ei成为常数.
英文摘要：
When I is an ideal of a standard graded algebra S with homogeneous maximal ideal \mm, it is known by the work of several authors that the Castelnuovo-Mumford regularity of I^m ultimately becomes a linear function dm + e for m \gg 0. We give several constraints on the behavior of what may be termed the \emph{regularity defect} (the sequence e_m = \reg I^m - dm). When I is \mm-primary we give a family of bounds on the first differences of the e_m, including an upper bound on the increasing part of the sequence; for example, we show that the e_i cannot increase for i \geq \dim(S). When I is a monomial ideal, we show that the e_i become constant for i \geq n(n-1)(d-1), where n = \dim(S).
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