Symbolic Powers of Classical Varieties

Let $R=\mathbb{K}[x_1,\dots ,x_n]$ and let ${\mathfrak{a}}_1,\dots ,{\mathfrak{a}}_m$ be homogeneous ideals satisfying certain properties, which include a description of the Noetherian symbolic Rees algebra. We give a solution to a question of Harbourne and Huneke for this set of ideals. We also 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.