Extreme values of the resurgence for homogeneous ideals in polynomial rings

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Harbourne, Brian¹  Kettinger, Jake¹  Zimmitti, Frank¹ 

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

关键词: Resurgence;    Asymptotic resurgence;    Symbolic power;    Integral closure of ideals;    Fat points;    Polynomial ring;   

DOI  :  10.1016/j.jpaa.2021.106811

来源: Elsevier

【 摘 要 】

We show that two ostensibly different versions of the asymptotic resurgence introduced by E. Guardo, B. Harbourne and A. Van Tuyl in 2013 are the same. We also show that the resurgence and asymptotic resurgence attain their maximal values simultaneously, if at all, which we apply to a conjecture of E. Grifo. For radical ideals of points, we show that the resurgence and asymptotic resurgence attain their minimal values simultaneously. In addition, we introduce an integral closure version of the resurgence and relate it to the other versions of the resurgence. In closing we provide various examples and raise some related questions, and we finish with some remarks about computing the resurgence. (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free