### Abstract

Iku Nakamura [Hilbert schemes of Abelian group orbits, J. Alg. Geom. 10 (2001), 757--779] introduced the G-Hilbert scheme for a finite subgroup G in SL(3,C), and conjectured that it is a crepant resolution of the quotient C^3/G. He proved this for a diagonal Abelian group A by introducing an explicit algorithm that calculates A-Hilb C^3. This note calculates A-Hilb C^3 much more simply, in terms of fun with continued fractions plus regular tesselations by equilateral triangles.

Original language | English |
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Title of host publication | Geometry of toric varieties |

Subtitle of host publication | S'eminaires et Congr`es |

Pages | 129-154 |

Volume | 6 |

Publication status | Published - 2002 |

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## Cite this

Craw, A., & Reid, M. (2002). How to calculate A-Hilb(C^3). In

*Geometry of toric varieties: S'eminaires et Congr`es*(Vol. 6, pp. 129-154)