  Symbolic powers of ideals have attracted interest in commutative algebra and
algebraic geometry for many years, with a notable recent focus on containment
relations between symbolic powers and ordinary powers. Several invariants have
been introduced and studied in the latter context, including the resurgence and
asymptotic resurgence.
  There have been exciting new developments in this area recently. It had been
expected for several years that $I^{Nr-N+1}\subseteq I^r$ should hold for the
ideal $I$ of any finite set of points in ${\bf P}^N$ for all $r>0$, but in the
last year various counterexamples have now been constructed, all involving
point sets coming from hyperplane arrangements. In the present work, we compute
their resurgences and obtain in particular the first examples where the
resurgence and the asymptotic resurgence are not equal.
