How to calculate A-Hilb C³
Craw, Alastair · Reid, Miles
Original · EN
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 C³/G. He proved this for a diagonal Abelian group A by introducing an explicit algorithm that calculates A-Hilb C³. This note calculates A-Hilb C³ much more simply, in terms of fun with continued fractions plus regular tesselations by equilateral triangles.
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