Non-reductive geometric invariant theory and Thom polynomials

TL;DR

This paper introduces a new approach to computing Thom polynomials of Morin singularities using non-reductive geometric invariant theory and equivariant localisation, simplifying previous complex models with combinatorial methods.

Contribution

It develops a novel intersection theory framework for non-reductive GIT quotients and derives explicit formulas for Thom polynomials using toric combinatorics.

Findings

Derived explicit formulas for Thom polynomials of Morin singularities.

Introduced a combinatorial approach that avoids complex Borel geometry.

Connected non-reductive GIT with intersection theory and localisation techniques.

Abstract

We combine recently developed intersection theory for non-reductive geometric invariant theoretic quotients with equivariant localisation to prove a formula for Thom polynomials of Morin singularities. These formulas use only toric combinatorics of certain partition polyhedra, and our new approach circumvents the poorly understood Borel geometry of existing models.