Symbolic powers via extension

Abstract This article investigates under which conditions symbolic powers of the extension of an ideal are the same as the extension of the symbolic powers. As an application, we prove formulas for the resurgence of sum of two homogeneous ideals in finitely generated graded $${\mathbbm {k}}$$ -algebras which are domains, where $${\mathbbm {k}}$$ is algebraically closed. Initially, these were known for homogeneous ideals in polynomial rings.