On the Craw-Ishii conjecture

Craw and Ishii proved that for a finite abelian group G in SL_3(C) every (projective) relative minimal model of C^3/G is isomorphic to the fine moduli space of \theta-stable G-constellations for some GIT parameter \theta. In this article, we conjecture that the same is true for a finite group G in GL_3(C) if a relative minimal model Y of X=C^3/G is smooth. We prove this for some abelian groups.