## How to calculate A-Hilb C^n for 1/r(a,b,1...1)

Sarah Davis, Timothy Logvinenko and Miles Reid

This website accompanies the paper
of the same name (37 pp., submitted to *the Rendiconti del
Circolo Matematico di Palermo, special Alg Geometry volume*).
All the material here should be presumed to be totally wrong, until
proven otherwise.

The original draft (4 pp.) of the paper,
potentially more lucid and useful than what it grew into.

A
text containing miscellaneous computations of *A-Hilb
C^4*,
conjectures/counterexamples arising thereof.
The
Magma code employed for these computations.

An example
of bad *A-Hilb*: for *A=1/30(1,6,10,13)* the *A-Hilb
C^4* is reducible.

Some
worked examples of the propellor game computations.

## Papers:

- Alastair Craw and Miles Reid,
“How to calculate
A-Hilb C^3”,

in *Ecole d'été sur les variétés toriques*
(Grenoble, 2000), collection Séminaires et Congrès, SMF 2001
- Iku Nakamura, “
Hilbert schemes of Abelian group orbits”,

*J. Algebraic Geom.* **10** (2001), 757–779
- Sarah Davis,
“Crepant resolutions and
A-Hilbert schemes in four dimensions”,

* University of Warwick Ph.D. thesis*, 127 pp., 2012
- Timothy Logvinenko, “Natural
G-Constellation Families”,

*Documenta Mathematica* **13** (2008), 803–823
- Timothy Logvinenko,
“Families of
G-Constellations parametrised by resolutions of quotient
singularities”,

* University of Bath Ph.D. thesis*, 140 pp., 2004

## Links:

Miles Reid's webpage on
McKay correspondence.