Positivity of Schur function expansions of Thom polynomials

TL;DR

This paper proves that the coefficients in Schur function expansions of Thom polynomials for certain singularities are nonnegative, using a combination of algebraic geometry and singularity theory techniques.

Contribution

It introduces a novel approach combining Kazarian's method and Fulton-Lazarsfeld positivity to establish nonnegativity of Schur function coefficients in Thom polynomials.

Findings

Coefficients of Schur function expansions are nonnegative for stable singularities.

The approach links classifying space methods with positivity theory.

Results apply to both stable and unstable singularities.

Abstract

Combining the Kazarian approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of numerical positivity for ample vector bundles, we show that the coefficients of various Schur function expansions of the Thom polynomials of stable and unstable singularities are nonnegative.