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 a and b b , we consider the set R e s ( a , b ) Res(a,b) of possible values of the resurgence of I + J I+J where I I and J J are ideals in disjoint sets of variables having resurgence a a and b b , respectively. Some questions and partial results about R e s ( a , b ) Res(a,b) are discussed.
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