Moduli of McKay quiver representations I: the coherent component

Craw, A., Maclagan, D. and Thomas, R.R. (2007) Moduli of McKay quiver representations I: the coherent component. Proceedings of the London Mathematical Society, 95(1), pp. 179-198. (doi: 10.1112/plms/pdm009)

Abstract

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

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Craw, Dr Alastair
• Authors: Craw, A., Maclagan, D., and Thomas, R.R.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the London Mathematical Society
• ISSN: 0024-6115
• ISSN (Online): 1460-244X
• Published Online: 30 March 2007