9 M ay 2 00 7 Thom polynomials and Schur functions : the singularities I 2 , 2 ( − )

The global behavior of singularities is governed by their Thom polynomials (cf. [35], [14], [1], [11], [31]). Knowing the Thom polynomial of a singularity η, denoted T η, one can compute the cohomology class represented by the η-points of a map. We do not attempt here to survey all activities related to computations of Thom polynomials, which are difficult tasks in general. In the present paper, following a series of papers by Rimanyi et al. [32], [31], [7], [2], we study the Thom polynomials for the singularities I2,2 of the maps (C•, 0) → (C•+k, 0) with parameter k ≥ 0. The way of obtaining the thought Thom polynomial is through the solution of a system of linear equations, which is fine when we want to find one concrete Thom polynomial, say, for a fixed k. However, if we want to find the Thom polynomials for a series of singularities, associated with maps (C•, 0) → (C•+k, 0) with k as a parameter, we have to solve simultaneously