  Let $R=\mathbb{K}[x_1,\dots,x_n]$ and $\mathfrak{a}_1,\dots,\mathfrak{a}_m$
are homogeneous ideals satisfying certain properties, which includes a
description of the Noetherian symbolic Rees algebra. Then, we compute the
Waldschmidt constant and resurgence and show that it exhibits a stronger
version of the Chudnovsky and Demailly-type bounds. We further show that these
properties are satisfied for classical varieties such as the generic
determinantal ideals, minors of generic symmetric matrices, generic extended
Hankel matrices, and ideal of pfaffians of skew-symmetric matrices.
