1D strata (S4Q) | 1D strata (TPQ) | Symmetries (QP&TU) | Modular Companions

This page is a code archive (Magma, Maple and Matlab) for projects focused on automorphisms and symmetries of Riemann surfaces. There are links to the relevant papers and code files. The code files or scripts, as I call them, are stored on a Google Drive dedicated to this purpose. Typically, the results of a script are stored as a .log text file. Aggregated results are sometimes given in a spreadsheet.

1. One dimensional equisymmetric strata in moduli space (S4Q actions – sphere quotient and 4 branch points)
Collaborators: Antonio F. Costa, UNED and Milagros Izquierdo, Linköping University
Link to paper: In this Comtemporary Math 776 Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics
Purpose of scripts: determine the braid classes of generating quadruples

Scripts and log files : 1. One dimensional strata – containing folder for the scripts and files below.

• braidquadclassnew.mgm – Magma package with variable definitions, record structures, and functions for determining braid classes of quadruples
• braidclass1.mgm – braid classes for general groups and a specific G-signature
• braidclass2.mgm – all braid classes and strata for a prime cyclic group
• braidclass3.mgm – all braid classes and strata for a cyclic group
• numstrata.xlsx – table of number of strata for prime cyclic groups
• Nonmax.mgm – determine if a stratum is non-maximal
• logfiles – folder for log files for the above scripts

2. One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces (TPQ actions – torus quotient with one branch point)
Collaborators: Antonio F. Costa, UNED, and Milagros Izquierdo, Linköping University.
Link to paper: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Purpose of scripts: classify and describe 1D strata described in the paper.

Scripts and log files : 2. Strata of surfaces with torus quotient and one puncture – containing folder for the scripts and files below

• TPQSurfStrataSearch.mgm – Magma Script for determining surfaces and strata for surfaces with torus-conepoint quotient (TPQ) for a range of action groups or an individual group.
• TPQSurfsStrata.xlsx – summary spreadsheet for TPQ surfaces and strata.
• TPQSurfStrataSearch-summary-counters-2-50.log – summary file for surfaces and strata for TPQ actions whose action group has order from 2 to 50.
• TPQSurfStrataSearch-summary-counters-51-100.log – summary file for surfaces and strata for TPQ actions whose action group has order from 51 to 100.
• TPQSurfStrataSearch-summary-counters-101-150.log – summary file for surfaces and strata for TPQ actions whose action group has order from 101 to 150.
• TPQSurfStrataSearch-summary-counters-151-200.log – summary file for surfaces and strata for TPQ actions whose action group has order from 151 to 200.
• logfiles – folder for log files for scripts

3. Quasiplatonic symmetries and triangulations of unorientable surfaces
Collaborator: Eduardo Brandani da Silva, Universidad Estatal de Maringa
Link to paper: Albanian Journal of Math 17(2) 105-142 2023.
Purpose of scripts: classify and describe symmetries described in the paper

Scripts and log files : 3 Quasiplatonic symmetries and triangulations of unorientable surfaces – containing folder for the scripts and files below

• SymmSearchAutoShort.mgm – Magma Script for determining symmetries on surfaces with triangular group action (quasiplatonic), for a range of groups or an individual group.
• SymmSearchResults.xlsx – summary spreadsheet for quasiplatonic symmetry data.
• SymmSearchShort-summary-counters-2-50.log – summary file for symmetries on surfaces whose action group has order from 2 to 50.
• SymmSearchShort-summary-counters-51-100.log – summary file for symmetries on surfaces whose action group has order from 51 to 100.
• SymmSearchShort-summary-counters-101-150.log – summary file for symmetries on surfaces whose action group has order from 101 to 150.
• SymmSearchShort-summary-counters-151-200.log – summary file for symmetries on surfaces whose action group has order from 151 to 200.
• SymmSearchShort-summary-counters-201-250.log – summary file for symmetries on surfaces whose action group has order from 201 to 250.
• logfiles – folder for log files for the scripts.

4. Modular companions in planar one-dimensional equisymmetric strata
Collaborators: Antonio F. Costa, Universidad Nacional de Educacion a Distancia and Milagros Izquierdo, Linkoping University
Link to paper: submitted
Purpose of scripts: Classify Aut(G) classes of actions of a group G with a given quotient type: sphere with 4 cone points or a torus with one cone point. Classify modular companions of a given action stratum. Compute size of maximal partial isometries between modular companions.
Scripts and log files : 4. Modular companions in planar one-dimensional equisymmetric strata – containing folder for the scripts and files below.

• ModCompCalcs.mgm – Magma Script for classifying modular companions, determining tiling defects, and computing partial isometries. Completes a total analysis for a group and signature (planar and toroidal). The group and signature specification must be provided in the script.
• ModCompFuncs.mgm – Magma Function file for the above calculation script. It must be loaded for the calculation script to work.
• logfiles – folder for log files for the scripts.