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arXiv · 2210.15606

A sharp bound for the resurgence of sums of ideals

Do Van Kien·Hop Dang Nguyen·Le Minh Thuan
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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. 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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Do Van Kien, Hop Dang Nguyen, Le Minh Thuan. 2022-10-27. A sharp bound for the resurgence of sums of ideals. https://arxiv.org/abs/2210.15606

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