Constructively describing orbit spaces of finite groups by few inequalities

Autor:	Moustrou, Philippe, Riener, Cordian, Schabert, Robin
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	Let $G$ be a finite group acting linearly on $\mathbb{R}^n$. A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space $\mathbb{R}^n /\!/G$ as a basic closed semi-algebraic set. We give a new proof of this statement and another description as a basic closed semi-algebraic set using elementary tools from real algebraic geometry. Br\"ocker was able to show that the number of inequalities needed to describe the orbit space generically depends only on the group $G$. Here, we construct such inequalities explicitly for abelian groups and in the case where only one inequality is needed. Furthermore, we answer an open question raised by Br\"ocker concerning the genericity of his result. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.08339 Zobrazit plný text záznamu View this record from Arxiv