Expected resurgence of ideals defining Gorenstein rings

TL;DR

This paper demonstrates that certain ideals defining Gorenstein rings exhibit expected resurgence, confirming the stable Harbourne Conjecture in specific algebraic settings, with results applicable in both prime characteristic and equicharacteristic zero.

Contribution

It establishes the expected resurgence of ideals defining Gorenstein rings under new conditions, extending previous work and covering cases in characteristic zero and prime characteristic.

Findings

Ideals defining Gorenstein rings have expected resurgence.

Stable Harbourne Conjecture holds for these ideals.

Results apply in both prime characteristic and equicharacteristic zero.

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.