How to calculate A-Hilb(C^3)

Alastair Craw; Miles Reid

How to calculate A-Hilb(C^3)

Alastair Craw
, Miles Reid

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

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.

Original language	English
Title of host publication	Geometry of toric varieties
Subtitle of host publication	S'eminaires et Congr`es
Pages	129-154
Volume	6
Publication status	Published - 2002

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title = "How to calculate A-Hilb(C\textasciicircum{}3)",

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\textasciicircum{}3/G. He proved this for a diagonal Abelian group A by introducing an explicit algorithm that calculates A-Hilb C\textasciicircum{}3. This note calculates A-Hilb C\textasciicircum{}3 much more simply, in terms of fun with continued fractions plus regular tesselations by equilateral triangles.",

author = "Alastair Craw and Miles Reid",

year = "2002",

language = "English",

volume = "6",

pages = "129--154",

booktitle = "Geometry of toric varieties",

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TY - CHAP

T1 - How to calculate A-Hilb(C^3)

AU - Craw, Alastair

AU - Reid, Miles

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

M3 - Book chapter

VL - 6

SP - 129

EP - 154

BT - Geometry of toric varieties

ER -

How to calculate A-Hilb(C^3)

Abstract

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