Non-associative Hilbert scheme and Thom polynomials

Abstract

Thom polynomial describes the cohomology class Poincaré dual to the locus of particular singularity of a generic holomorphic map. In this paper we derive a closed formula for the generating function of its coefficients. The method is based on a new construction of the embedding space of punctual Hibert scheme that we call the non-associative Hilbert scheme. The efficiency of the method is demonstrated on explicit computation of a number of Thom polynomials, including those associated with singularities of Thom-Boardman types~${\Sigma }^{i,j}$, ${\Sigma }^{2,1,1}$, ${\Sigma }^{2,2,1}$, and~${\Sigma }^{2,2,2}$.

29pp

References in corpus (2)

• Thom polynomials and Schur functions I
• Thom polynomials for maps of curves with isolated singularities

Cited by in corpus (2)

• On the basic structure theorems of global singularity theory
• On the rationality of the singularities of the $A_2$-loci