Algebraic Geometry Seminar

Catherine St-Pierre, University of Waterloo

Sheppard-Todd-Chevalley theorem (and beyond)

Sheppard-Todd-Chevalley's theorem is one of the most significant results in invariant theory. It provides necessary and sufficient conditions for the fixed subring k[x_1, \dots , x_n]^G under a finite subgroup G of GL_n(k) to be a polynomial ring. We will review the theorem and its applications and summarise some generalisations.