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.Comment: 14 pages, 01 figur