On the rationality of the singularities of the $A_2$-loci

Abstract

The rationality of the singularities of the $A_n$-loci is the natural question that arises in the papers devoted to the study of the Thom polynomials and $K$-theoretic invariants of the said loci. In this paper we prove that, in general, the $A_2$-loci have singularities worse than rational, and therefore they can not be presented as a GIT quotient of a smooth variety with respect to a reductive group.

References in corpus (2)

• Non-associative Hilbert scheme and Thom polynomials
• On the basic structure theorems of global singularity theory