Thom Polynomials of Morin Singularities

We begin with a quick summary of the notions of global singularity theory and the theory of Thom polynomials. For a more detailed review we refer the reader to [1, 15]. Let N and K be two complex manifolds of dimensions n and k respectively; assume that n ≤ k. Consider a holomorphic map f : N → K for which the differential d fp : TpN → TpK at a generic point p ∈ N is nonsingular, i.e. has rank n. Often, the topology of the situation forces f to have singularities at some points of N; this means that there will be p ∈ N where rank(d fp) < n. To introduce a finer classification of such singular points, choose local coordinates near p ∈ N and f (p) ∈ K, and consider the resulting germ of a map