Expected resurgences and symbolic powers of ideals

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.

arXiv commentFinal version to appear in the Journal of the London Mathematical Society

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Cited by in corpus (2)

• The Initial Degree of Symbolic Powers of Fermat-like Ideals of Planes and Lines Arrangements
• On the stable Harbourne conjecture for ideals defining space monomial curves