On resurgence via asymptotic resurgence

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