Dihedral G-Hilb via representations of the McKay quiver

TL;DR

This paper explicitly describes the G-Hilb of C^2 for small binary dihedral groups using G-graphs and quiver representation moduli spaces, providing a detailed geometric construction.

Contribution

It introduces a new explicit description of G-Hilb(C^2) for small binary dihedral groups via G-graphs and quiver representation theory.

Findings

Explicit affine open cover of G-Hilb(C^2) constructed

Classification of G-graphs applied to describe the moduli space

Provides a detailed geometric and algebraic framework for G-Hilb

Abstract

For a given small binary dihedral group G we use the classification of G-graphs to describe explicitly G-Hilb(C^2) by giving an affine open cover of M(Q,R), the moduli space of stable quiver representations.