论文标题
限制单一理想的理性力量的行为
Limit Behavior of the Rational Powers of Monomial Ideals
论文作者
论文摘要
我们研究理想的理性力量。我们发现，在单一理想的情况下，规范的索引导致了理性力量的特征，从而产生了无方形单样理想的符号力量确实是理性的力量本身。使用与符号功率技术的连接，我们使用分割来显示深度和标准化Castelnuovo-Mumford的规律性的收敛性。我们显示了斯坦利深度为理性力量的融合，因此，我们显示了整体闭合力量的史丹利深度的前面未知的融合。此外，我们还显示了渐近相关的素数的有限性，我们发现局部同胞模块的归一化长度会融合理性的力量，因此具有无形的单一理想的符号力量。
We investigate the rational powers of ideals. We find that in the case of monomial ideals, the canonical indexing leads to a characterization of the rational powers yielding that symbolic powers of squarefree monomial ideals are indeed rational powers themselves. Using the connection with symbolic powers techniques, we use splittings to show the convergence of depths and normalized Castelnuovo-Mumford regularities. We show the convergence of Stanley depths for rational powers, and as a consequence of this we show the before-now unknown convergence of Stanley depths of integral closure powers. In addition, we show the finiteness of asymptotic associated primes, and we find that the normalized lengths of local cohomology modules converge for rational powers, and hence for symbolic powers of squarefree monomial ideals.
