Title: Finite Parts of Certain Divergent Integrals and Their Dependence on Regularization Data

Abstract: Let $X$ be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on $X$ that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle $E \rightarrow X$. We consider two different regularizations of such integrals, both depending on a choice of smooth Hermitian metric on $E$. Given such a choice, for each of the two regularizations there is a natural way to define a finite part of the divergent integral, and we show that they coincide. Our main result is an explicit formula for the dependence on the choice of metric of the finite part.