Expected resurgence of ideals defining Gorenstein rings

Authors

Eloísa Grifo, University of Nebraska-LincolnFollow
Craig Huneke, University of VirginiaFollow
Vivek Mukundan, Indian Institute of Technology Delhi,Follow

Date of this Version

6-2020

Citation

arXiv:2007.12051v2 [math.AC] 27 Jul 2020

Comments

Copyright © 2020 by the authors

Abstract

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.