Equations of Riemann surfaces with automorphisms
Supplementary files for the paper "Equations of Riemann surfaces with
automorphisms" by David Swinarski
Here is the most
recent draft of the paper and the most
recent version of my Magma code for this
project.
Matrix generators of irreducible representations of finite
groups
In the paper I state an algorithm suggested by Valery Alexeev and
James McKernan to produce matrix generators of an irreducible
representation of a finite
group given its character.
In these notes we work out
an example: the two-dimensional irreducible representation of the
symmetric group \(S_3\).
Equations of genus 4, 5, 6, or 7 Riemann surfaces with large automorphism groups
- Equations of genus 4 Riemann surfaces
with large automorphism groups
- Equations of genus 5 Riemann surfaces
with large automorphism groups
- Equations of genus 6 Riemann surfaces
with large automorphism groups
- Equations of genus 7 Riemann surfaces
with large automorphism groups
Getting started
The four lists above contain 69 examples. If you want to look at a small
number of examples to get a feeling for what can happen, I suggest
the following:
- Genus 7, automorphism group
(64,41) is the example used in the paper
- Genus 4, automorphism group
(72,40) is a relatively simple example
- Genus 7, automorphism group
(48,41) is one of the most complicated examples (the
flattening stratification has a five-dimensional base space), yet it still results
in simple equations
- Genus 7, automorphism group
(504,156) (Macbeath's curve) is an example where the
output of my program is almost comically complicated, compared to Macbeath's equations
