  The resurgence and asymptotic resurgence of an ideal in a polynomial ring are
two statistics which measure the relationship between its regular and symbolic
powers. We address two aspects of resurgence which can be studied via
asymptotic resurgence. First, we show that if an ideal has Noetherian symbolic
Rees algebra then its resurgence is rational. Second, we derive two bounds on
asymptotic resurgence given a single known containment between a symbolic and
regular power. From these bounds we recover and extend criteria for the
resurgence of an ideal to be strictly less than its big height recently derived
by Grifo, Huneke, and Mukundan. We achieve the reduction to asymptotic
resurgence by showing that if the asymptotic resurgence and resurgence are
different, then resurgence is a maximum instead of a supremum.
