论文标题
通过渐近复苏复兴
On resurgence via asymptotic resurgence
论文作者
论文摘要
多项式环中理想的复兴和渐近复发是两个统计数据，它们衡量了其规则和符号能力之间的关系。我们解决了复苏的两个方面，可以通过渐近复苏进行研究。首先，我们表明，如果一个理想具有no noterian象征性的里斯代数，那么它的复兴是理性的。其次，鉴于象征性和规则功率之间的单个已知遏制，我们在渐近复苏上得出了两个界限。从这些界限中，我们恢复并扩展了理想的复兴，严格比Grifo，Huneke和Mukundan最近得出的高度少了。我们通过表明渐近复苏和复兴是不同的，那么我们将减少到渐近恢复，那么复兴是最大而不是上超级人。
The resurgence and asymptotic resurgence of an ideal in a polynomial ring are two statistics which measure the relationship between its regular and symbolic powers. We address two aspects of resurgence which can be studied via asymptotic resurgence. First, we show that if an ideal has Noetherian symbolic Rees algebra then its resurgence is rational. Second, we derive two bounds on asymptotic resurgence given a single known containment between a symbolic and regular power. From these bounds we recover and extend criteria for the resurgence of an ideal to be strictly less than its big height recently derived by Grifo, Huneke, and Mukundan. We achieve the reduction to asymptotic resurgence by showing that if the asymptotic resurgence and resurgence are different, then resurgence is a maximum instead of a supremum.
