# Hyperplane arrangements associated to symplectic quotient singularities

## TL;DR

This paper explores the connection between hyperplane arrangements and symplectic quotient singularities, revealing new insights into their representation theory and conditions for smooth Calogero-Moser spaces.

## Contribution

It establishes an equivalence between hyperplane arrangements from minimal model program and CM-hyperplanes from rational Cherednik algebras, with implications for representation theory.

## Key findings

- Hyperplane arrangements match those from rational Cherednik algebras.
- Calogero-Moser space is smooth iff families are trivial.
- Descriptions of arrangements for exceptional complex reflection groups.

## 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.