A sharp bound for the resurgence of sums of ideals

TL;DR

This paper establishes a precise upper bound for the resurgence of sums of ideals with disjoint variables, advancing previous conjectures and providing complete solutions for specific cases.

Contribution

It introduces a sharp bound for the resurgence of sums of ideals and resolves two conjectures related to this bound.

Findings

Derived a sharp upper bound for resurgence of sums of ideals

Provided complete solutions for two conjectures by Bisui--Hà--Jayanthan--Thomas

Analyzed the set of possible resurgence values Res(a,b) for ideals with given resurgence

Abstract

We prove a sharp upper bound for the resurgence of sums of ideals involving disjoint sets of variables, strengthening work of Bisui--H\`a--Jayanthan--Thomas. Complete solutions are delivered for two conjectures proposed by these authors. For given real numbers $a$ and $b$, we consider the set Res$(a,b)$ of possible values of the resurgence of $I+J$ where $I$ and $J$ are ideals in disjoint sets of variables having resurgence $a$ and $b$, respectively. Some questions and partial results about Res$(a,b)$ are discussed.