How to calculate A-Hilb(C^3)

Alastair Craw, Miles Reid

Research output: Chapter or section in a book/report/conference proceedingChapter or section


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 languageEnglish
Title of host publicationGeometry of toric varieties
Subtitle of host publicationS'eminaires et Congr`es
Publication statusPublished - 2002


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