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Moduli of McKay quiver representations I: the coherent component |
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| Authors: | Craw Alastair; Maclagan Diane; Thomas Rekha R |
| Institution: | 1 Department of Mathematics University of Glasgow Glasgow G12 8QW United Kingdom craw{at}maths.gla.ac.uk 2 Department of Mathematics Hill Center — Busch Campus Rutgers University 110 Frelinghuysen Road Piscataway, NJ 08854 USA maclagan{at}math.rutgers.edu 3 Department of Mathematics University of Washington Seattle, WA 98195 USA thomas{at}math.washington.edu |
| Abstract: | For a finite abelian group G  GL (n,  ), we describe the coherent component Y of the moduli space  of-stable McKay quiver representations. This is a not-necessarily-normaltoric variety that admits a projective birational morphism  obtained by variation of GeometricInvariant Theory quotient. As a special case, this gives a newconstruction of Nakamura's G-Hilbert scheme HilbG that avoidsthe (typically highly singular) Hilbert scheme of |G|-pointsin  . To conclude, we describe the toric fan of Y and hence calculate the quiver representationcorresponding to any point of Y. |
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