Suppose that $X$ is a closed irreducible subvariety of ${\Bbb P}^n$ (possibly singular). If $\rho\in {\Bbb N}$ is larger than a concretely given constant, the authors of the paper under review prove a quite explicit division-interpolation formula for sections of the restriction of ${\Cal O}(\rho)$ to $X$. \par If $V$ is an algebraic subvariety of ${\Bbb C}^n$ such that its closure in ${\Bbb P}^n$ is irreducible, this division-interpolation formula allows the authors to give a more explicit version of the Briançon-Skoda-Huneke type theorem proved by M.~E.~L. Andersson and E. Wulcan in [Invent. Math. {\bf 200} (2015), no.~2, 607--651; MR3338011].