Singularidades de curvas definidas por anéis de representação

Abstract

Let G be a finite group of order n, and (..) an n-th primitive root of the unity. Consider the affine curve (..) where R(G) is the representation ring of G. We study the fibers of the formal tangent sheaf of C by estimating their dimension and also finding (and measuring) the singularities of C. We carefully deal with three simple examples of noncommutative groups, targeting an algorithm to compute these invariants in general.