Reflection maps

Abstract

Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied in terms of the group action. We give obstructions to A-stability and A-finiteness of reflection maps and produce, in the unobstructed cases, infinite families of finitely determined map-germs of any corank. We relate these maps to conjectures of Lê, Mond and Ruas.