Hyperplane arrangements associated to symplectic quotient singularities

Abstract

We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangement of CM-hyperplanes coming from the representation theory of restricted rational Cherednik algebras. We explain some of the interesting consequences of this identification for the representation theory of restricted rational Cherednik algebras. We also show that the Calogero–Moser space is smooth if and only if the Calogero–Moser families are trivial. We describe the arrangements of CM-hyperplanes associated to several exceptional complex reflection groups, some of which are free.