The containment problem for the ideal of fatted general points in $\mathbb{P}^2$

Let $W=\{p_1, p_2, \dots, p_s\}$ be a configuration of $s\ge 3$ general points in $\mathbb{P}^2$. Let $Z$ be the scheme defined by the ideal $I(Z)=I(p_1)^{(s-2)} \bigcap I(p_2) \bigcap\dots \bigcap I(p_s)$. In this note, the containment problem for the ideal I(Z)$ is investigated and among the other things, the numerical invariants of $.I$, i.e., the resurgence, the Waldschmidt constant and the regularity of the ideal $I$ is computed .