Moduli of G-constellations and crepant resolutions II: The Craw–Ishii conjecture

For any given finite subgroup G ⊂ SL3(C), we show that every projective crepant resolution X of the quotient variety C3/G is isomorphic to the moduli space of Θ-stable G-constellations for a generic stability condition Θ, as conjectured by Craw and Ishii. We also show that generators of the Cox ring of X can be obtained from semi-invariants for representations of the McKay quiver of G.