This project arose from my work decomposing Jacobian varieties of
curves since in that work I needed to know the generating vectors for a given
group acting on a curve. Thomas Breuer had programs which computed this
information, but he did not record it with data he generated from those programs. I have added functionality to his
program to record these generating vectors, and run the programs in Magma
and GAP up to genus 48. The data for these generating vectors is below.
The details of this project may be found in this writeup
[pdf] and also posted on
I have no plans to publish this work, as it is just a
modification of Breuer's original work. If you use the generating vector data, you can cite this page or the ArXiV
page mentioned above. I would love to hear from you if you use it.
Finally, thank you to Thomas Breuer for giving me permission to repost
Breuer's code, translated to Magma and modified to print generating vectors. Last Modified: May 10, 2016 genvectors.m
My code to read the data into Magma, or search the data for specific types
of examples. Last Modified: April 24, 2016 searchroutines.m
Groups and Signatures only
This file gives the list of groups and signatures for all genus from 2 to
48, except two curves of genus 46 of size 2160. It is simply a compliation of data Breuer created,
updated for the larger current Magma or GAP databases. Last Modified: December 23, 2015 groupsignaturedata (2.7 MB)
Magma: large groups
For genus g from 2 to 48, this gives the generating vectors for all groups
of order greater than 4(g-1) (again except for the genus 46
examples of size 2160). Last Modified: December 23, 2015 GenVectMagma-LargeGps
(2.5 MB zipped)
WARNING: This data was computed using Magma V2.19-9. Changes in newer versions of Magma mean that in a couple of cases
an error may be returned. I am working on a permanent fix, but in the short term, if you run into an error and are
running a newer verion of Magma, email me
and I can give you a workaround. Thanks to Michela Artebani and her student, Cristian Monsalve, at Universidad de Concepcion for
pointing out the issue.
In genus 46 there is are two groups acting on curves of this genus but which
are beyond the size of the SmallGroup database. Their information is
recorded here. g46_2160
Magma: complete data for genus 2 through 20
For genus g from 2 to 20, this gives the generating vectors for all
groups. Last Modified: May 16, 2016
Email me if you would like access to this 44.0 MB zipped file.
WARNING: See the warning under the previous section.
GAP: full data to genus 40
This is the full data for GAP. Currently up to genus 40, except genus 33. Last Modified: December 23, 2015
Email me if you would like access to t his 40.9 MB zipped file.
Magma: other available versions
Full data for higher genus is available upon request.