2025/03/12 by Richárd Rimányi, Rimanyi, Richard
Computer Science · Mathematics · #14C17 #14E15 #32S20 #58K45 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2503.09809
openalex publication_date 2025/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thom polynomials provide universal formulas for the fundamental class 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 analogs of these axioms within a degree-bounded framework, we obtain new 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.