Thom polynomials and Schur functions: the singularities I_{2,2}(-)

TL;DR

This paper computes Thom polynomials for the singularity class I_{2,2} using restriction equations and Schur functions, advancing the understanding of singularity theory in complex maps.

Contribution

It introduces a novel combination of restriction equations and Schur functions to explicitly compute Thom polynomials for I_{2,2} singularities.

Findings

Explicit Thom polynomials for I_{2,2} singularities are obtained.

The method integrates restriction equations with Schur function techniques.

Results enhance computational tools in singularity theory.

Abstract

We give the Thom polynomials for the singularities $I_{2,2}$ associated with maps $({\bf C}^{\bullet},0) \to ({\bf C}^{\bullet+k},0)$ with parameter $k\ge 0$. Our computations combine the characterization of Thom polynomials via the ``method of restriction equations'' of Rimanyi et al. with the techniques of Schur functions.