Symbolic Powers of Ideals Defining F-pure and Strongly F-regular Rings. (11th September 2017)

• Record Type: Journal Article
• Authors: Grifo, Eloísa; Huneke, Craig
• Is Part Of: International mathematics research notices. Volume 2019:Number 10(2019)
• Page Start: 2999
• Page End: 3014
• Publication Date: 2017-09-11
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx213
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Given a radical ideal $I$ in a regular ring $R$, the Containment Problem of symbolic and ordinary powers of $I$ consists of determining when the containment $I^{(a)} \subseteq I^b$ holds. By work of Ein–Lazersfeld–Smith, Hochster–Huneke and Ma–Schwede, there is a uniform answer to this question, but the resulting containments are not necessarily best possible. We show that a conjecture of Harbourne holds when $R/I$ is F-pure, and prove tighter containments in the case when $R/I$ is strongly F-regular.