# Expected resurgences and symbolic powers of ideals

## TL;DR

This paper provides explicit criteria to determine when the resurgence of a self-radical ideal is less than its codimension, leading to new results on symbolic powers and applications to space monomial curves.

## Contribution

It introduces explicit criteria for the resurgence of certain ideals and applies these to families including space monomial curves, advancing understanding of symbolic power containments.

## Key findings

- Resurgence of self-radical ideals can be explicitly bounded.
- Criteria imply the stable Harbourne's conjecture for these ideals.
- New bounds for symbolic powers of space monomial curves.

## Abstract

We give explicit criteria that imply the resurgence of a self-radical ideal in a regular ring is strictly smaller than its codimension, which in turn implies that the stable version of Harbourne's conjecture holds for such ideals. This criterion is used to give several explicit families of such ideals, including the defining ideals of space monomial curves. Other results generalize known theorems concerning when the third symbolic power is in the square of an ideal, and a strong resurgence bound for some classes of space monomial curves.