Relative fundamental class in Deligne cohomology and application (Q1817307)

Let \(S\) be a reduced complex analytic finite-dimensional space and \(X\) the graph of local analytic family \((X_s)_{s\in S}\) of \(n-\)cycles of complex analytic manifold \(Z\) parametrized by \(S.\) The objective of this article is to construct the \(S\)-relative fundamental class of the family \((X_s)_{s\in S}\) in Deligne cohomology.