Non-compensation of local contributions for the maximal asymptotic currents (Q1354741)

The asymptotic expansion near \(s=0\) of the function \(F_\varphi(s)=\int_{\{f=s\}}\varphi\), where \(\varphi\) is a \(C^\infty\) differential form of type \((n,n)\) on an analytic manifold \(X\), carries geometric information about the holomorphic map \(f:X\rightarrow \mathbb{C}\). The author solves the problem of non-vanishing currents for such expansions and succeeds in computing explicitly the currents for the case when \(\{f=s\}\) is a normal crossing divisor. He then applies the results when studying the local contributions for maximal asymptotic currents. The main result of non-compensation of the local contributions of the currents applies for any hypersurface singularity, not necessarily isolated.