How to calculate A-Hilb C³

1999/09/15 by Alastair Craw, Craw, Alastair, Miles Reid +1 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9909085

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

arxiv created 2001/09/13 · arxiv updated 2009/11/30

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 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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