Moduli of McKay quiver representations I: the coherent component

Abstract

For a finite abelian group G in GL(n,k), we describe the coherent component Y_theta of the moduli space M_theta of theta-stable McKay quiver representations. This is a not-necessarily-normal toric variety that admits a projective birational morphism to A^n/G obtained by variation of GIT quotient. As a special case, this gives a new construction of Nakamura's G-Hilbert scheme that avoids the (typically highly singular) Hilbert scheme of |G|-points in A^n. To conclude, we describe the toric fan of Y_theta and hence calculate the quiver representation corresponding to any point of Y_theta.

22 pages, 5 figures. Final version, to appear in Proceedings of the LMS

References in corpus (4)

• McKay equivalence for symplectic resolutions of singularities
• Families of G-constellations over resolutions of quotient singularities
• Geometrical McKay Correspondence for Isolated Singularities
• Fan is to monoid as scheme is to ring: a generalization of the notion of a fan