Moduli of McKay quiver representations I: the coherent component
Algebraic Geometry
2011-01-13 v2 Commutative Algebra
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.
Cite
@article{arxiv.math/0505115,
title = {Moduli of McKay quiver representations I: the coherent component},
author = {Alastair Craw and Diane Maclagan and Rekha R. Thomas},
journal= {arXiv preprint arXiv:math/0505115},
year = {2011}
}
Comments
22 pages, 5 figures. Final version, to appear in Proceedings of the LMS