Interpolation characterization of higher Thom polynomials
Abstract
Thom polynomials provide universal expressions for the fundamental classes of singularity loci in terms of characteristic classes. Ohmoto extended this notion to SSM-Thom polynomials, which refine this description by capturing the richer Segre–Schwartz–MacPherson (SSM) class of singularity loci. While previous methods for computing SSM-Thom polynomials relied on intricate geometric arguments, we introduce a more efficient approach that depends solely on the symmetries of singularities. Our method is inspired by connections to geometric representation theory, particularly the interpolation properties of Maulik–Okounkov stable envelopes. By formulating SSM analogues of these axioms within a degree-bounded framework, we obtain new, surprisingly simple computational tools for SSM-Thom polynomials. We also present explicit examples of SSM-Thom polynomials, and illustrate their applications in enumerative geometry and singularity theory.
