Thom polynomials and Schur functions I

TL;DR

This paper computes Thom polynomials for specific singularities using Schur functions, providing explicit expansions and analyzing approximations to these polynomials.

Contribution

It introduces explicit Thom polynomial formulas for I_2,2 and A_3 singularities and extends analysis to A_i singularities with Schur function techniques.

Findings

Explicit Schur function expansions for Thom polynomials of I_2,2 and A_3.

Analysis of the first approximation F^(i) for A_i singularities.

Combination of restriction equations and Schur functions for computations.

Abstract

We give the Thom polynomials for the singularities I_2,2 and A_3 associated with maps (C^n,0) -> (C^{n+k},0) with parameter k>=0. We give the Schur function expansions of these Thom polynomials. Moreover, for the singularities A_i (with any parameter k >= 0) we analyze the ``first approximation'' F^(i) to the Thom polynomial. Our computations combine the characterization of Thom polynomials via the ``method of restriction equations'' of Rimanyi et al. with the techniques of (super) Schur functions.