Work

Equivariant algebraic and semi-algebraic geometry of infinite affine space

Year: 2024

Type: article

Abstract: We study Sym ( ∞ ) -orbit closures of non-necessarily closed points in the Zariski spectrum of the infinite polynomial ring C [ x i j : i ∈ N , j ∈ [ n ] ] . Among others, we characterize invariant prime ideals in this ring. Furthermore, we study projections of basic equivariant semi-algebraic sets defined by Sym ( ∞ ) orbits of polynomials in R [ x i j : i ∈ N , j ∈ [ n ] ] . For n = 1 we prove a quantifier elimination type result which fails for n > 1 .

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2024.11.016

Authors: Mario Kummer, Cordian Riener

Institutions: Technische Universität Dresden, UiT The Arctic University of Norway

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

Funders: Trond Mohn stiftelse, Tromsø Forskningsstiftelse