How to calculate A-Hilb C^3
Algebraic Geometry
2007-05-23 v2
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.
Cite
@article{arxiv.math/9909085,
title = {How to calculate A-Hilb C^3},
author = {Alastair Craw and Miles Reid},
journal= {arXiv preprint arXiv:math/9909085},
year = {2007}
}
Comments
Minor corrections, 32 pp. with 13 figures plus activity pack. To appear in Ecole d''et'e sur les vari'et'es toriques (Grenoble, 2000), collection S'eminaires et Congr`es, SMF 2001