How to calculate A-Hilb C^3

Details How to calculate A-Hilb C^3 How to calculate A-Hilb C^3

1999-09-15

arxiv.org/abs/math/9909085v2

Mathematics

Algebraic Geometry

Minor corrections, 32 pp. with 13 figures plus activity pack. To appear in Ecole d''et'e sur les vari'et'es toriques (Grenoble

Scientific paper

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.

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