Let $A$ be a unital ring. Suppose $I\subset A$ is an ideal. Clearly $I\subset\sqrt{I}\subset A$. Suppose $A$ is noetherian or $I$ is f.g. Furthermore assume $\sqrt{I}\subset\sqrt{J}$ for some ideal $J\subset A$. Since $I$ is f.g., there is a minimal $m$ s.t. $I^m\subset J$.
$\textbf{Q:}$ Is there geometric meaning associated to this minimal $m$? And what is the geometric meaning of nilpotent elements in $A/I$? Is this $m$ supposed to be chart independent as well in complex geometric setting?