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generic-stabs

https://github.com/alunik/generic-stabs

Science Score: 44.0%

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  • Host: GitHub
  • Owner: alunik
  • Default Branch: main
  • Size: 15.6 KB
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Created almost 2 years ago · Last pushed over 1 year ago
Metadata Files
Readme Citation

readme.md

Generic Stabilizers for Actions of Algebraic Groups

A resource for the computational search of generic stabilizers

Given the action of an algebraic group $G$ on a variety $Y$, one of the most fundamental ways to understand the action is to determine its generic behaviour, if it exists. Informally, there is a generic behaviour if there is an open dense subset of the variety where the action behaves the same on all elements.

More precisely, there is a generic stabilizer $S\leq G$ for the action of $G$ on $Y$, if there is a dense open subset $U$ of $Y$ such that for all $u\in U$ the stabilizer $G_u$ (the isotropy group of $u$) is $G$-conjugate to $S$.

Using MAGMA

Magma is a computer algebra software that can be extremely helpful to execute computations for algebraic groups over finite fields. The name of the game is guess the generic stabilizer by computing stabilizers over small finite fields.

In this resource, I share my strategies and code I have used to tackle this question.

Owner

  • Name: Aluna Rizzoli
  • Login: alunik
  • Kind: user
  • Company: EPFL

Scientist at EPFL

Citation (citation.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
  - family-names: Aluna
    given-names: Rizzoli 
    orcid: https://orcid.org/0000-0003-1501-3501
title: "Magma code used for computations"
version: 0.1
identifiers:
  - type: doi
    value: 10.5281/zenodo.13134216
date-released: 2024-30-07
repository-code: "https://github.com/alunik/generic-stabs"

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