On the rationality of the singularities of the A₂-loci

2017/12/10 by Natalia Kolokolnikova, Kolokolnikova, Natalia
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1712.03558

openalex publication_date 2017/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 A₂-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.

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