Enumerating stationary multiple-points (Q1106909)

Let f: \(X\to Y\) be a morphism of schemes. A point \(x_ 1\in X\) is said to be an r-fold point iff there exist points \(x_ 2,...,x_ r\) with the same image as x. If some of the points \(x_ i\) lie infinitely near, then \(x_ 1\) is said to be a stationary r-fold point. Under suitable hypothesis of finiteness and genericity on f, the author enumerates stationary r-fold points of f. More precisely, if \(a=(a_ 1,...,a_ s)\) is a partition of r, denote by \(N_ a\) the locus of points \(x_ 1\in X\) such that there are points \(x_ 2,...,x_ r\) with the same image and \(a_ 1-1\) of these points lie infinitely near \(x_ 1\), \(a_ 2\) of these points lie infinitely near each other, and so on. Then the author finds an intersection-theoretic class \(n_ a\) whose support is \(N_ a\) and gives formulas for \(n_ a\) in terms of the invariants of f.