Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces (Q1433425)

Suppose \(M\) is a two-dimensional complex manifold and \(f\) is a holomorphic selfmap of \(M\) that fixes pointwise a singular, compact, reduced and globally irreducible curve \(C\subset M\). When \(f\) is nondegenerate on \(C\), the authors define a residual index for \(f\) at each point of \(C\). Furthermore, the authors prove that the sum of the indices is equal to the selfintersection number of \(C\).