A sharp bound for the resurgence of sums of ideals

Kien, Do; Nguyen, Hop; Thuan, Le

doi:10.1090/proc/16655

A sharp bound for the resurgence of sums of ideals
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by Do Van Kien, Hop D. Nguyen and Le Minh Thuan

Proc. Amer. Math. Soc. 152 (2024), 1405-1418

DOI: https://doi.org/10.1090/proc/16655

Published electronically: January 26, 2024

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Abstract:

We prove a sharp upper bound for the resurgence of sums of ideals involving disjoint sets of variables, strengthening work of Bisui–Hà–Jayanthan–Thomas [Collect. Math. 72 (2021), pp. 605–614]. 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.

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