A-Hilb A4 in Magma and the (1, 2)-symmetric project
An algorithm calculates A-Hilb A4 for a finite diagonal subgroup
A in SL(4,C).
A-Hilb is a toric scheme (not necessarily irreducible, normal or even
reduced).
The function ASets(r, A) returns a list of monomial ideals that form its
0-dimensional
strata. The toric fan of A-Hilb consists of cones that are the dual
of the monomial
bases modulo these ideals. This is analysed explicitly for the
(1,2)-symmetric
groups. This still needs to be written up in prose and diagrams, but
the algorithms in
this file ASets
works reliably, and runs in
the online Magma calculator
in a few
seconds for groups A of order up to about 50.
This file
contains Magma routines that analyse A-Hilb A4 for a (1,2)-symmetric
group A and prints out the toric fan of A-Hilb. Instructions are
given at the start.
Click here for sample output
as graphics
There is also a 2009 partial
write-up of the A-Sets algorithm. This has known errors
and omissions, and describes the 2009 version of the algorithm.
In particular,
the 2023 upgrade works with 1/r(a,b,c,d) without requiring a=1.